# Trigonometric Identities Teacher Resources

Find Trigonometric Identities lesson plans and worksheets

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Lesson Planet

#### Graphing Trig Functions

Going from simple trig functions to their graphs can seem like a daunting task. These resources show the steps to connect evaluating the functions to graphing them. The collection has a variety of resource types for you to explore.

EngageNY

#### EngageNY Algebra II Module 2: Trigonometric Functions

Building on young mathematicians prior knowledge of geometry and algebraic functions, this 17-lesson unit introduces the topic of trigonometric ratios. Starting with the basic definitions of sine, cosine, and tangent, students move on to...

Lesson Planet

#### Getting into Trig

Starting with right triangles (SOH-CAH-TOA) and working up to the concept of radians, this collection introduces students to trigonometric ratios and supports them in learning to evaluate trigonometric functions.

Lesson Planet

#### High School Math Handouts

A collection of different resources can augment any math curriculum. Sheets can be printed, posted on the wall, or emailed to students for use in the classroom.

Lesson Planet

#### Trigonometric Ratios with a Calculator: Lesson

Calculators ... they are more efficient than tables. Using two 30-60 right triangles, the segment of a playlist on geometry shows that trigonometric ratios for an angle are the same independent of the size of the triangle. The video...

Lesson Planet

#### Worksheet 9: Trig Functions

In this math worksheet, students are given 7 problems in which they write expressions for trig functions, compute limits and graph functions.

Lesson Planet

#### Inverse Trig Functions

Learners solve and graph 10 different problems that are the inverses of various trig functions. First, they determine which equation is equivalent to a given equation. Then, they find an angle of a right triangle, given its leg lengths....

Lesson Planet

#### Trigonometric Ratios: A Geometer's Perspective

What do all right triangles have in common? Young mathematicians investigate the trigonometric ratios in relation to right triangles. Their investigations lead to a hypothesis they use to determine unknown lengths in different triangles.

Lesson Planet

#### Exact Trigonometric Ratios: Triangles to the Unit Circle

Special right triangles give special information. Individuals learn how to find trigonometric ratios in all quadrants. This involves using special right triangles and the Pythagorean Theorem.

EngageNY

#### Proving Trigonometric Identities

Young mathematicians first learn the basics of proving trigonometric identities. They then practice this skill on several examples.

Lesson Planet

#### The Trigonometric Ratios: Lesson

SOH, what is this thing called trigonometric ratios? A section of an extensive playlist on geometry identifies the adjacent and opposite sides in relationship of an angle. Using the identified sides, the video defines the sine, cosine,...

Lesson Planet

#### Intro to Trigonometric Ratios

Finding trigonometric ratios is relatively easy; you just have to know where to look. The first installment of a 16-part video playlist shows how to find the sine, cosine, and tangent values for a given angle. It shows how to find the...

Lesson Planet

#### Trigonometric Identities and Laws

Your learners will appreciate this handy resource when they are working with various trigonometry problems. The most common trigonometric identities and laws are all typed on one page.

Lesson Planet

#### 6.5 Skill Builder: Trigonometric Identities

In this trigonometric identities worksheet, students solve 16 multi-part short answer problems. Students use the quotient identity and Pythagorean identity to simplify trigonometric expressions. Students factor trigonometric expressions.

Lesson Planet

#### Discovering Trigonometric Ratios

Are there equivalent ratios in right triangles? The discovery lesson has the class find the ratios of sides of right triangles with equivalent angle measurements. Using these ratios, pupils discover that particular ones are the same,...

Lesson Planet

#### Inverse Trigonometric Ratios: Lesson

Finding the inverse of trigonometric ratios is not the same as finding the reciprocal. The presentation introduces how to find the angle of a right triangle given sides. Part of a larger playlist on geometry, the video uses the inverse...

Lesson Planet

#### Trig Functions

In this trig functions worksheet, students solve and complete 24 different types of problems. First, they find the limits for each trig function given. Then, students find xso that the given infinities series converges. They also find...

Lesson Planet

#### Are You Pulling My Trig?

Build on students' knowledge about triangles with this introductory lesson on trigonometric ratios. After first exploring key terms in a scavenger hunt activity, students solve a series of guided and independent practice problems dealing...

EngageNY

#### The Definition of Sine, Cosine, and Tangent

Introduce your classes to a new world of mathematics. Pupils learn to call trigonometric ratios by their given names: sine, cosine, and tangent. They find ratios and use known ratios to discover missing sides of similar triangles.

Lesson Planet

#### Worksheet #2: Trigonometric Ratios

In this trigonometric ratios worksheet, students use trigonometric ratios to complete indirect measurement word problems. This three-page worksheet contains 3 problems.

EngageNY

#### Basic Trigonometric Identities from Graphs

Have young mathematicians create new identities! They explore the even/odd, cofunction, and periodicity identities through an analysis of tables and graph. Next, learners discover the relationships while strengthening their understanding...

Lesson Planet

#### Trigonometric Ratios

In this trigonometric ratios worksheet, 10th graders solve 9 different problems that include determining the trigonometric ratios of each triangle. First, they determine the sides and angles of a right triangle that is shown in each...

Lesson Planet

#### Trig Identities

In this trig identities learning exercise, students solve and complete 25 various types of problems. First, they assume that sine and cosine are given as stated. Then, students express the stated quantities in terms of a and b for each...

Lesson Planet

#### Trigonometric Ratios

In this trigonometric ratios worksheet, students find the sine, cosine and tangent of given triangles. Students determine the angle measurement or length of one side of a triangle. This two-page worksheet contains 43 problems. Each page...

Lesson Planet

#### Trigonometric Ratios

In this trigonometric ratios worksheet, 11th graders solve and complete 15 different types of problems. First, they use the unit circle to sketch the line through an angle with a given measure. Then, students find the coordinates of a...

Lesson Planet

#### Basic Trigonometric Ratios

In this trigonometric ratio worksheet, students determine the length of a side of a right triangle, or the measurement of angles using trigonometric ratios. This one-page worksheet contains 24 problems. Answers are provided at the bottom...

Lesson Planet

#### Proof of Identity

Students explore trigonometric identities. In this Algebra II lesson, students use graphing to verify the reciprocal identities. Using Cabri Jr, students investigate the Pythagorean trigonometric identities and the geometric c proofs...

Lesson Planet

#### Does Your Field Measure Up

Young scholars measure angles using a plane table kit. In this geometry lesson, students use trigonometric identities to find the values of the length of a football field.

Lesson Planet

#### Finding Trigonometric Ratios

In this finding trigonometric ratios worksheet, 11th graders solve and complete 22 various types of problems. First, they find the value of each trigonometric ratio to the nearest ten-thousandth. Then, students use a calculator to find...

Lesson Planet

#### Trigonometric Ratios: Sine

What happens when you don't have enough information to use the Pythagorean Theorem? Time for some trig! The second lesson in a series of four introduces the definition of sine, teaches how to find the sine ratio of a right triangle, and...

Lesson Planet

#### Chain Rule for Derivatives, with Trig Functions

Break the chain in finding derivatives of trigonometric functions. The short video provides a demonstration of finding the derivative of a trigonometric function where the argument is a function. The 12th video in a series of 31 focuses...

Lesson Planet

#### Differentiation Quiz

In this differentiation quiz worksheet, students solve 10 short answer problems. Students differentiate rational equations, trig functions, exponential models, higher order polynomials, etc.

Lesson Planet

#### Trigonometric Ratios

In this trigonometric ratios worksheet, students determine the value of trigonometric ratios. They find the area of triangles, determine the length of one side, and compute the degrees in an angle. This five-page worksheet contains 55...

Lesson Planet

#### "I Saw the Sine"

Discover trigonometric ratios that complement each other. Using two videos, the lesson introduces the trigonometric ratios. The class discovers the relationship between the sine and cosine of complementary angles.

Lesson Planet

#### Trigonometric Function

For this trigonometric functions worksheet, 11th graders solve and complete 6 various types of problems. First, they express each of the expressions in trigonometric form. Then, students use DeMoivre's Theorem to express each of the...

Lesson Planet

#### Intro to the Trigonometric Ratios

This video introduces the basics of trigonometry. It starts by defining a right triangle and showing two different examples of finding the ratios of sine, cosine, and tangent using the SOH-CAH-TOA mnemonic. This resource could be used as...

Lesson Planet

#### Exploring Trigonometric Ratios

Students identify the ratios of trig functions. In this trigonometry lesson, students construct triangles and use it to derive the values of sine, cosine and tangent. They use Cabri software to create the visual of the identities.

Lesson Planet

#### Inverse Trig Functions: Domain and Range

In this trigonometric functions worksheet, students calculate the domain and range of the three basic trig functions. There are 6 equations.

Lesson Planet

#### Trigonometric Ratios and the Pythagorean Theorem

Take an alternative route with trigonometry and let learners connect a tweaked version of the pythagorean theorem to the original in terms of triangle sides. The assignment leads participants towards deriving the Pythagorean identity...

Lesson Planet

#### SOHCAHTOA - Finding Missing Sides Part 1

Explore the meaning and application of the three trigonometric ratios. A thorough video reviews the trig ratios and then shows how to apply them in triangle problems. The instructor demonstrates several examples finding both side and...

Lesson Planet

#### Introduction to SOHCAHTOA

You might not be able to pronounce it, but everyone remembers SOHCAHTOA. Young mathematicians learn a way to remember the three major trigonometric ratios. They see how the first letters of certain words lead to the mnemonic.

Lesson Planet

#### The Cosine Ratio

Help your classes understand the relationship between trigonometric ratios and similarity. A set of questions ask scholars to consider the ratio of sides of similar figures. They conclude that all similar triangles must have the same...

Lesson Planet

#### Trig Card Game (Review of Trig Identities)

For this trig card game, learners play a card game to form and identify trigonometric identities. Students collect cards to form identities. This one-page worksheet contains instructions for making cards and the rules of the game. ...

Lesson Planet

#### Special Values of Trig Functions

For this trig functions worksheet, students complete a chart to find the special values of trig functions. This one-page worksheet contains 58 problems.

Lesson Planet

#### Section 5.2 Worksheet: Trig Functions

In this trig function worksheet, students find the values of six trig functions for the given angle. They determine the exact values of the legs of right triangles. Students use the Pythagorean identities to write expressions as an...

Lesson Planet

#### Practice B: Trigonometric Ratios

In this trigonometric ratios instructional activity, students use trigonometric ratios to determine the length of one side of a triangle or the angle measurement of right triangles. They draw vectors in a coordinate plane. This...

Lesson Planet

#### Trig Ratios

Students derive the six trigonometric ratios. In this trigonometry activity, students use trigonometric properties to find the missing angles of triangles.

Lesson Planet

#### Ratios in Right Triangles

Learners calculate the sides of right triangles in this trigonometric ratios lesson. They use Cabri Jr. software and TI-83 or TI-84 calculators to find the side lengths and their ratios to each other for various triangles. The provided...

Lesson Planet

#### The unit circle definition of trigonometric function

In this video, Sal shows how the sine and cosine of an angle are defined on the unit circle. He inscribes a 30-60-90 triangle in the unit circle and explains how one can use SOH-CAH-TOA to find the coordinates on the circle.

Lesson Planet

#### Verifying Trigonometric Identities

This quality, short, worksheet provides practice verifying trigonometric identities and completing the included blank unit circle. Learners will also find the exact value of various trigonometric functions given other trigonometric...

Lesson Planet

#### Limits of Trig Functions: Everything You Need to Know!

Discover how to find limits of trigonometric functions. Viewers learn a strategy to calculate limits of trigonometric functions. They see how an expression can be rewritten to one whose limits are already known.

Lesson Planet

#### Decoding Basic Trigonometric Ratios

Demonstrate the calculator keystrokes necessary for finding a measure of an angle using trigonometry. A straight forward lesson explains how to calculate an angle measure given a sine, cosine, or tangent ratio. The narrator discusses...

Lesson Planet

#### Trigonometry Identity Review/Fun

In this video, Sal derives a number of trigonometric identities. Starting with the sum of angles formula for sine and cosine, Sal proves a number of other identities including the double-angle formulas, the difference of angles formulas,...

Lesson Planet

#### Exercise Set 5.1: Trigonometric Functions of Real Numbers

In this trig functions worksheet, students find the trig values of 46 problems. Students find the trig values of various radian measures. Students use trig properties to prove trig identities.

Lesson Planet

#### Trig Derivatives

In this trig derivatives instructional activity, students find the derivative of a given trigonometric function. This one-page instructional activity contains 16 multi-step problems.

Lesson Planet

#### Graphing Trig Functions

In this graphing trig functions worksheet, students find the amplitude of each function. They graph the function. This four-page worksheet contains 12 problems. Answers are provided on the last two pages.

Lesson Planet

#### Review of Trig Ratios

For this trigonometric ratios worksheet, students solve and complete 10 various types of problems. First, they write the degrees listed in radian measure. Then, students find the exact ratios for each equation. They also find the value...

Lesson Planet

#### Functions, Domains and Composites

In this functions, domains and composites activity, students solve and complete 23 various types of problems. First, they graph the given trigonometric function on a coordinate plane. Then, students label three points on each graph and...

Lesson Planet

#### Trig Cheat Sheet

Your pre-calculus learners will make use of this wonderful cheat sheet that summarizes all things trigonometric. Definitions based on both the unit circle and the right triangle are included, as well as many convenient trigonometric...

Lesson Planet

#### Fun Trig Problem

If solving trigonometric equations is your idea of fun, then this video is correctly titled. Here Sal uses trigonometric identities, the quadratic formula, and inverse trigonometric functions to solve a trigonometric equation sent in by...

Lesson Planet

#### Fun Trig Problem

Lesson Planet

#### Similar Parts Investigation

How tall is that flagpole? Your pupils might want to stand on each other's shoulders to answer this, but this activity is all about using the math knowledge they already possess. Using right triangle trigonometric ratios (SOH CAH TOA)...

Lesson Planet

#### How Tall is It?

Your collaborative geometry learners use trigonometric ratios and a clinometer that they assemble themselves to indirectly measure the height of a flag pole and other objects. Then they create a presentation to explain the process they...

Lesson Planet

#### Surveying the Ancient World

Astrolabes have been used by explorers and astronomers throughout the ages. But how exactly do they work and what can a young mathematician do with one today? Students will build a simple version of this tool and then using the altitude,...

Lesson Planet

#### Indirect Measurement Technique: Using Trigonometric Ratios

Students explore the concept of trigonometric ratios. In this trigonometric ratios lesson, students use trigonometric ratios and the angle of elevation/depression to determine the height of an object. Students use their clinometer made...

Lesson Planet

#### Section 8-6: Solving Problems Using Trigonometric Ratios

In this trigonometric ratios worksheet, students solve 20 short answer and multiple choice problems. Students use trigonometric ratios, the angle of depression, and angle of elevation to find missing side lengths of angles of a triangle.

Lesson Planet

#### Trig Identities Part 3 (Part 5 if you watch the proofs)

Sal takes the mystery out of the trigonometric identities by showing how easily they can be derived. He continues with a problem he started in the video �Trig identities part three (part five if you watch the proofs) and proves the trig...

Lesson Planet

#### 2003 AIME ll Problem 11.avi

Sal solves an interesting problem from the American Invitational Mathematics Exam from 2003 that uses the Pythagorean Theorem, knowledge of geometric principles of triangles, and the use of trigonometric identities.

Lesson Planet

#### 2004 AIME ll Problem 14

In an involved problem from the American Invitational Mathematics Exam from 2004, Sal logically shows the multi-step solution. He uses geometric properties of hexagons, parallelograms, and triangles, trigonometric identities, and the...

Lesson Planet

#### Fundamental Trigonometric Identities: Tangent Identity

An identity that thieves can't steal the tangent identity. Scholars manipulate ratios to investigate the tangent ratio and connect it to the sine and cosine ratios. An interactive that uses color coding helps with this task.

Lesson Planet

#### Right Triangle Trigonometry: Evaluating Trigonometric Ratios

For this right triangle trigonometry worksheet, students use trigonometric ratios to determine the length of a missing side of a triangle or to find a specified angle measurement. This four-page worksheet contains 32 problems. Answers...

Lesson Planet

#### Evaluating Trig equations and Solving Trig Identities

In this trigonometry worksheet, students match trig expressions to their exact value, evaluate trig equations, graph trig equations, and prove trig identities. There are 61 questions.

Lesson Planet

#### Trigonometric Function

In this trigonometric function worksheet, 10th graders solve and complete 26 various types of problems. First, they use a calculator to find each value and each angle. Then, students state which trig function they used to find each given...

Lesson Planet

#### Trig Functions of General Angles

In this trigonometric functions worksheet, 11th graders solve and complete 19 various types of problems. First, they find the exact value of the six trig functions of the terminal side in standard position contains the given point. Then,...

Lesson Planet

#### Trigonometry Chapter 2 Test

In this trigonometry test, students use trigonometric ratios to solve problems. They find the exact trigonometric function value, solve right triangle problems, and real-life application problems. This two-page worksheet contains 30...

Lesson Planet

#### Inverse Trig Functions: Arccos

In the third video on inverse trigonometric functions, Sal follows a format similar to the last two. He finds the value for the arcos (-1/2) and shows the restricted domain of the arccos function. He also finds the value for cos(arccos...

Lesson Planet

#### Inverse Trig Functions: Arcsin

Sal defines the concept of inverse trigonometric functions and completes two examples of arcsin. Specifically, he finds the value of the arcsin (sqroot2/2) and arcsin (sqroot3/2). He also talks about the restricted domain of arcsin...

Lesson Planet

#### Inverse Trig Functions: Arctan

Continuing with inverse trigonometric functions, Sal finds the value for tan^-1-1. He also shows the restricted domain of the arctan function.

Lesson Planet

#### Applications of Trigonometric Functions

Using trigonometric ratios to solve geometry and application problems is the focus of this detailed problem set and solution presentation. The presentation covers many ways to use trigonometry, from finding missing measures in right...

Lesson Planet

#### Trigonometry Review Sheet

Get the trig facts fast, and use the review sheet as a guide in the classroom. The worksheet also includes a document version if any changes are needed to the problems. The information includes a small degree/radian chart, a graph of all...

Lesson Planet

#### Trig Transformations

Learners investigate trigonometric function. In this Algebra II lesson, students explore functional notation and transformational graphing of trigonometric functions.

Lesson Planet

#### Module 7: Trigonometric Functions, Equations, and Identities

Show your class that trigonometric functions have characteristics of their own. A resource explores the features of trigonometric functions. Learners then connect those concepts to inverse trigonometric functions and trigonometric...

Lesson Planet

#### Trig Tour

Unit circles and trigonometric graphs go hand in hand. Pupils see how traversing the unit circle allows for the creation of graphs for trigonometric functions. They also see trigonometric ratios in terms of the ordered pairs of points on...

Lesson Planet

#### The Trigonometric Functions

This extensive chapter gives learners a new angle on that old geometry favorite, trigonometry. From the unit circle to right triangles, the role of trigonometric ratios is explored through explanation of theory and working application...

Lesson Planet

#### Are You Pulling My Trig?

Introduces the three main trigonometric ratios to your class. Pupils use a calculator to determine the sine, cosine, and tangent of given angles and side ratios. They continue on to use the ratios to solve problems.

Lesson Planet

#### Similarity and Right Triangle Trigonometry

Starting with similar triangles and dilation factors, this unit quickly and thoroughly progresses into the world of right triangle features and trigonometric relationships. Presented in easy-to-attack modules with copious application...

EngageNY

#### Trigonometry and the Pythagorean Theorem

Ancient Egyptians sure knew their trigonometry! Pupils learn how the pyramid architects applied right triangle trigonometry. When comparing the Pythagorean theorem to the trigonometric ratios, they learn an important connection that...

Lesson Planet

#### Hopewell Geometry

The Hopewell people of the central Ohio Valley used right triangles in the construction of earthworks. Pupils use the Pythagorean Theorem to determine missing dimensions of right triangles used by the Hopewell people. The assessment task...

Lesson Planet

#### ADA Accessibility

Ramp up using trigonometric ratios. After receiving a request to check school ramps to verify they meet ADA requirements, groups calculate the angle of the incline on ramps on campus. They report their findings via a letter to the...

EngageNY

#### Unknown Angles

How do you solve an equation like trigonometry? Learners apply their understanding of trigonometric ratios to find unknown angles in right triangles. They learn the meaning of arcsine, arccosine, and arctangent. Problems include basic...

Lesson Planet

#### Special Right Triangles and Right Triangle Trigonometry

Right triangles are so special! Use special right triangles to discover the trigonometric ratios. Pairs construct special right triangles and find the values of the ratios of the sides. In the process, they discover the ratios stay the...

Lesson Planet

#### Smarter Balanced Sample Items: High School Math – Target O

Trigger an increased understanding of trigonometry. Young mathematicians answer a set of questions that require finding trigonometric ratios using similarity and solving real-world problems involving trigonometry. The questions all come...

Lesson Planet

#### Indirect Measurement Technique: Using Trigonometric Ratios

Ninth graders create clinometers using a protractor, weight, and string. They work in pairs to practice sighting objects above or below their line of sight. Students use ratios of right triangles to determine the height of a...

Lesson Planet

#### Inverse Trig Functions

Students solve problems using trig identities. In this trigonometry lesson, students evaluate inverse trig functions and relate it to the unit circle and determine the domain and range of the inverse trigonometric functions

Lesson Planet

#### Trigonometry Review

In this trigonometry worksheet, students solve trigonometric equations, prove trigonometric identities, and graph trigonometric functions. The four page worksheet contains sixteen questions. Answers are not included.

Lesson Planet

#### Trigonometric Functions

In this trigonometric functions activity, students graph a given trigonometric function. This one-page activity contains 1 problem. Graph paper is included.

Lesson Planet

#### Complimentary Angles

In this complimentary angles worksheet, 11th graders solve and complete 12 various types of problems. First, they express as a co-function of a complimentary angle. Then, students find the exact values using the sum and differences...

Lesson Planet

#### 13-7 Skills Practice: Inverse Trigonometric Functions

In this inverse trigonometric function activity, students write the inverse of a function. They solve inverse functions and write angle measures in radians. This one-page activity contains 24 problems.

Lesson Planet

#### Integrated Algebra: State Exam

In this integrated algebra worksheet, students solve problems related to topics covered in algebra for the entire year. Topics include, but are not limited to, inequalities, probability, functions, interval notation, exploring graphs,...

Lesson Planet

#### Review Quiz before Mini-Exam

In this pre-calculus review worksheet, students solve 28 multiple choice problems. Students find the trigonometric values of various angles, find the eccentricity of an ellipse, use trigonometric identities solve compounded interest...

Lesson Planet

#### Solving Problems Using Trigonometric Ratios and the Pythagorean Theroem

In this geometry worksheet, 10th graders use right triangle trigonometry and the Pythagorean Theorem to solve application problems. The six page worksheet contains multi-part questions. Answers are not included.

Lesson Planet

#### Unit Circle & Trig Functions

In this trig functions worksheet, students determine the exact value of given trigonometric functions. They label degrees, radians and coordinates of given points on a circle. This two-page worksheet contains approximately 20 multi-step...

Lesson Planet

#### Limits of Trig Functions

In this trigonometry worksheet, students solve 14 problems with trig functions by calculating and solving for the limit.

Lesson Planet

#### Trigonometric Functions: The Unit Circle

This comprehensive problem and note set walks the class through a large part of simplifying trigonometric expressions using the unit circle and identities. From identifying angles to applying appropriate trigonometric ratios, problems...

EngageNY

#### Properties of Trigonometric Functions

Given a value of one trigonometric function, it is easy to determine others. Learners use the periodicity of trigonometric functions to develop properties. After studying the graphs of sine, cosine, and tangent, the lesson connects them...

Lesson Planet

#### Reciprocal Identities

Get a better understanding of the trigonometric functions by taking a look at the flip side. Pupils create angles within a unit circle and compare the values of the standard trigonometric functions to their reciprocal functions. The...

Lesson Planet

#### Basic Trigonometric Functions: Ladder Length

Climb the ladder to trigonometry. The interactive introduces trigonometric ratios and finding lengths of sides of right triangles created by a ladder and a building. Learners use the interactive to create triangles by moving the top of...

Lesson Planet

#### Pythagorean Theorem for Solving Right Triangles: Solving the Triangle

Observe the change in the trigonometric ratios as angles vary. An interactive provides the values of trigonometric ratios for both acute angles in a right triangle. Pupils create a right triangle to match given criteria and find the...

Lesson Planet

#### Finding the Area of an Equilateral Triangle

The problem seems simple: find the area of the equilateral triangle whose sides are each length 1. In fact, this same problem is solved in 8th grade, addressing a different Common Core standard, using the formula for area of a triangle...

EngageNY

#### Incredibly Useful Ratios

Start the exploration of trigonometry off right! Pupils build on their understanding of similarity in this lesson that introduces the three trigonometric ratios. They first learn to identify opposite and adjacent sides before exploring...

EngageNY

#### End-of-Module Assessment Task - Geometry (module 2)

Increase the level of assessment rigor with the test of performance tasks. Topics include similar triangles, trigonometric ratios, Law of Sines, Law of Cosines, and trigonometric problem solving.

EngageNY

#### Algebra II Module 2: Mid-Module Assessment

Time for classes to show what they've learned. Use several tasks to assess understanding of the trigonometric functions, unit circle, radians, and basic trigonometric identities.

Lesson Planet

#### Trigonometry Word Problems: Lesson

Look up or down to find the answer. A segment of an extensive playlist on geometry introduces angle of depression and elevation to find indirect measurements. Using trigonometric ratios, the presentation finds missing sides and angles...

Lesson Planet

#### Introduction to Trigonometry

The topic of trigonometric ratios is often covered with loads of rote memorization baked into the activity. This activity set, however, leans more on using similar triangles and discovery learning to help young geometers develop a deeper...

Lesson Planet

#### Washington Monument

Look up, up, up to the top. Using their knowledge of trigonometric ratios, pupils determine the angle of elevation in a real-world situation. Learners calculate the angle of elevation from the base of the flags around the Washington...

Lesson Planet

#### The Pythagorean Theorem

There isn't a more popular geometry formula than the Pythagorean Theorem! Learners understand the special side relationships in a right triangle. They use the Pythagorean Theorem to find missing sides and to solve problems. They begin...

Lesson Planet

#### Length of a Chord: Distance Across a Ferris Wheel

An interactive presents two friends on a ferris wheel with the task of finding the distance between the them. Pupils create the chord between the two friends and calculate its lengths using trigonometric ratios.

Lesson Planet

#### Introduction to SOHCAHTOA

Explore right triangle trigonometry with a thorough video lesson. The lesson instructor introduces the trigonometric ratios with an examination of right triangle sides and angles. She continues with practice writing the ratios using...

Lesson Planet

#### Patterns in the 30-60-90 Table

Sine and cosine ratios have more in common than just their names—they are complementary to each other. Using a 30-60-90 triangle, pupils create a table of the sine and cosine of the acute angles. The learners describe the relationships...

Lesson Planet

#### How to Build a Happy Home

Build a complete house in just a few days. Learners create floor, roof, deck, and landscape plans for a two-story house. Scholars then use their knowledge of area formulas, trigonometric ratios, and the Pythagorean Theorem to determine...

Lesson Planet

#### Trigonometric Integrals

Present examples of trigonometric integrals with a video that shows an example of determining a trigonometric integral. The AP Calculus example shows that many of the trigonometric integrals require manipulation and using trigonometric...

Lesson Planet

#### Basic Trigonometry ll

Sal continues with examples of finding the sine, cosine, and tangent of an angle in a right triangle using SOH-CAH-TOA. In his examples, he reviews the use of the Pythagorean Theorem and rationalizing the denominator of a fraction. He...

Lesson Planet

#### Trigonometric Ratios

In this trigonometric ratio worksheet, learners find the length of legs on a right triangle and determine the value of specified angles in a triangle. Notes and explanations are given prior to the exercises. This three-page worksheet...

Lesson Planet

#### Powers of Trig Functions

In this trigonometric worksheet, students solve integrals by substitution and the Pythagorean theorem. Students use their trigonometric functions to solve problems. This four-page worksheet contains 20 problems.

Lesson Planet

#### Inverse Trig Functions: Chain Rule

In this trigonometric functions worksheet, students differentiate inverse trigonometric functions using the chain rule. There are 15 questions.

Lesson Planet

#### How Tall Is It?

Find the height from afar. Teams role play as summer interns to find the height of a set of windows from the outside. Scholars must first determine how to find the height with the available tools. After determining a strategy involving...

Lesson Planet

#### Trigonometry – Missing Sides

If it's missing, then find it. Young mathematicians watch a video that explains how to solve for a missing side of a right triangle. They then complete a worksheet on the topic. The use of trigonometric ratios is expected here.

Lesson Planet

#### Connect The Dots Trig. Identities

In this trig. identities worksheet, learners connect the dots to equivalent values. Then students find the isosceles right triangle formed. Solutions are provided.

Lesson Planet

#### Derivatives of Trig Functions

What are the most important things about trigonometric derivatives? The 13th video in a series of 31 highlights three important aspects of trigonometric derivatives, the first being the derivatives of sine and cosine. The second is the...

Lesson Planet

#### Round and Round We Go

Connect the dots on trigonometry with K'nex. Scholars use a K'nex model of a Ferris wheel to collect data points to plot on a height versus time graph. They'll then consider what type of function best models the data in the graph—and...

Lesson Planet

#### Derivatives of Inverse Trig Functions - Arcsin

Put another link in the chain. With the aid of the chain rule, the presentation shows how to take the derivative of an arcsin function with a binomial argument. The 15th video in a 31-part series goes on to work through the...

Lesson Planet

#### Derivatives of Inverse Trig Functions - Arccot

Get two functions for the cost of one. The short video is the 16th in a series of 31 video on calculus topics. The presenter works through finding the derivative of a function involving two arccot functions. One of the functions requires...

Lesson Planet

#### Differentiation Quiz Form B

In this differentiation worksheet, students differentiate 10 functions in short answer format. Students differentiate trig, logarithmic, cubic, exponential, rational, and higher order functions.

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#### Trigonometric Identities

In this trigonometry worksheet, learners derive the 6 different trigonometric identities. They use the identities to solve problems by multiplication of trig ratios. There are 102 trig questions to be solved.

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#### Graphing Trig Functions

In this graphing trigonometric functions worksheet, 11th graders solve and complete 10 various types of problems. First, they graph each functions as shown. Then, students find the domain in each given function. In addition, they find...

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#### Facilitated Remembrance of Trig Functions

Students review the trigonometric functions of sine, cosine, and tangent. They foster expertise with the secant, cosecant, and cotangent functions. Students invent a story about CHOSHACAO and her special relationship with SOHCAHTOA.

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#### Trigonometric Functions

In this trigonometric functions worksheet, students solve and complete 35 various type of problems. First, they find the values for all six trig functions that pass through the given points. Then, students prove different identities as...

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#### Trig Ratios of General Angles

In this trig ratios worksheet, students determine the angle measurement of trigonometric ratios. They find the value of trigonometric function. This approximately four-page worksheet contains 24 problems. Answers are provided on the last...

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#### Trigonometry Ratios

Students identify the different angles and sides of a triangle. In this geometry lesson plan, students identify the six trigonometric ratios. They graph the graph of each trig function and analyze it.

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#### When is Tangent, tangent?

High schoolers study the concept of tangent of a unit circle. In this unit circle instructional activity, students explore the mathematical history of the trigonometric ration, tangent, through an interactive date-gathering construction...

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#### Applied Trigonometry Problems

In this applied trigonometry problems instructional activity, students solve 12 short answer word problems. Students use trigonometric ratios to find angles of elevation and depression. Students find distances between objects using...

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#### Right Triangle Applications: Lessons 1 and 2

Use right triangles for more than just mathematical problems. The first two lessons of a unit ask pupils determine distances between cities by using the Pythagorean Theorem and a map. To cement understanding, learners use trigonometric...

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#### Circular Trigonometric Functions

In this Pre-calculus/Trigonometry learning exercise, students prove trigonometric identities and find all values that satisfy the equations of circular trigonometric functions. The four page learning exercise contains twenty-four...

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#### What are the Trigonometric Reciprocal Identities?

By using the trigonometric ratios in a right triangle, the instructor derives definitions for cosecant, secant, and cotangent.

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#### How Tall Am I?

Which method results in a better estimate of the height? Using different methods, groups estimate the height of three objects on campus. They record their measurements and any necessary computations and compare them to the actual...

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#### Similar Right Triangles and Trig Ratios

Is it possible to be the same yet different? Absolutely! The activity asks learners to explore the relationships between side ratios of triangles they have drawn. Because individuals all draw a triangle with the same angle measures, they...

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#### Graphing the Tangent Function

Help learners discover the unique characteristics of the tangent function. Working in teams, pupils create tables of values for different intervals of the tangent function. Through teamwork, they discover the periodicity, frequency, and...

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#### Trigonometric Identities

Investigate the properties of a Unit Circle, wahoo! Your class will memorize the basic identities of sine, cosine, and tangent. Then those smart cookies can investigate the negative of an angle measure using sine and cosine. Included are...

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#### Graphs of the OTHER Trig Functions

Students graph trigonometric functions. In this precalculus lesson, students identify the properties of secant ,cosecant and cotangent. They use the unit circle as their formula to graph and analyze these functions.

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#### Section 5.3 Worksheet: Trig Functions

In this trig functions worksheet, students find the exact values of intervals that satisfy an equation. They graph trig functions and use a formula for negatives to find the exact value. This two-page worksheet contains 13 multi-step...

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#### Trigonometry: Labeling, Formulas, Solving

In this math worksheet, students label sides of right triangles as opposite, hypotenuse, and adjacent to the labeled angle. On the second page of the worksheet, students label the part of the right triangle marked with a question mark...

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#### Trigonometry

In this right triangles worksheet, students use trigonometric ratios to determine the length of a side of a triangle or a missing angle measurement. This two-page worksheet contains 20 problems.

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#### Using Trinonometry to Find Angle Measures

In this trigonometric ratios worksheet, learners find the missing angle of 20 triangles by using sine, cosine and tangent ratios. Students compute the angle measurement of given ratios for six problems.

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#### Right Angle Triangles an the Cosine Ratio

In this right triangle worksheet, students use trigonometric ratios to find the missing measurement of right triangles. This nine-page worksheet contains 10 multi-step problems. Answers are provided at the end of the worksheet.

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#### Trigonometry Homework

In this right angles worksheet, learners use trigonometric ratios to determine the length of a missing side or a missing angle of a right triangle. This two-page worksheet contains 19 problems.

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#### Right Triangles Trigonometry

The class uses the computers to access GeoGebra Dynamic Worksheets to learn the basics about vectors. They will look at graphs and make computations to problem solve to find coordinates of vectors.

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#### Trig Identities Part 2 (Part 4 if you watch the proofs)

In this video, Sal reviews the basic trigonometric definitions and identities including the sum of angles formulas and then derives the double angle formulas.

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#### Understanding Fundamental Trigonometric Identities

Students are introduced to the basic trigonometric identities. Using a diagram, they discover why the parts of the unit circle as named as they are and use equations to finalize the Pythagorean trigonometric identities. They also review...

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#### Give Me a Sine

High schoolers link the use of trigonometric ratios to the use of trigonometric functions. Students contribute sets of data points to build the graphs of the sine and cosine functions. Worksheet and activity is included with this lesson.

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#### Investigating Trigonometric Ratios Through Similar Right Triangles

Pupils identify similar and congruent right triangles. In this geometry lesson plan, students use trigonometric ratios to identify missing sides and angles of a triangle. They differentiate similar and congruent triangles.

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#### Discovering Inverse Trig Functions

In this trigonometry worksheet, learners use a graphing calculator to graph trig functions and their inverses. The one page worksheet contains three questions. Answers are not provided.

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#### Right Triangles

In this right triangles worksheet, 10th graders solve and complete 39 different problems. First, they find the missing variables and trigonometric ratios. Then, students select the correct ratio from the four ratios provided for each...

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#### Review 13.1-13.2: Unit Circle

For this unit circle worksheet, students find the sine, cosine, tangent, cotangent, and co-secant of given values. They determine the exact value of trigonometric ratios. Students convert from degrees to radians. This two-page worksheet...

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#### Test 2: MAT 104 - Trigonometry

For this trigonometry worksheet, learners use trigonometric ratios and the Pythagorean Theorem to find the length of one side of a triangle. They determine values of angles and solve story problems. This two-page worksheet contains 25...

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#### Trigonometry

This trigonometry textbook takes the learner from a basic understanding of angles and triangles through the use of polar coordinates on the complex plane. Written by a mathematician-engineer, examples and problems here are used to...

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#### Right Triangle Trigonometry

Practice manipulating trigonometric functions, cofunctions, inverses, and applications is the name of the game in this short but extensive problem set. Starting with the Pythagorean Theorem and basic applications, then progressing...

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#### Trigonometric Functions

From a circle to a cycle! The final lesson of a five-part series challenges learners to use points from the unit circle to plot a repeating pattern. The repeating patterns become the graphs of the trigonometric functions. Scholars also...

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#### Derivatives of Trigonometric Functions: Derivative of sin(x)

Graphically find the derivative of sin(x). Using the interactive, pupils graph the slope of the tangent line to the sine function. Class members use the resulting graph to determine the derivative of the sine function. They verify their...

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#### The Robotic Arm

Working as teams, class members try to rescue an astronaut using the shuttle arm on a TI-Nspire simulation. Teams must determine the different angle measures in order to reach the stranded astronaut.

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#### Basic Trigonometry and Radians

A fabulous set of examples and problems that introduce basic trigonometry concepts, this packet is set apart by the care it takes to integrate both radians and degrees into the material. After defining radians, the author demonstrates...

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#### Secant, Cosecant, and Cotangent Functions: Hold the Ladder!

Determine the length of a falling ladder. Pupils use an interactive to find the angle a ladder makes with the floor after it falls to answer questions. The scholars use the triangle formed in the interactive to determine values of...

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#### Eratosthenes and the Circumference of the Earth

The class gets to practice being a mathematician in ancient Greece, performing geometric application problems in the way of Eratosthenes. After following the steps of the great mathematicians, they then compare the (surprisingly...

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#### Solving Problems Using Sine and Cosine

Concepts are only valuable if they are applicable. An informative resource uses concepts developed in lessons 26 and 27 in a 36-part series. Scholars write equations and solve for missing side lengths for given right triangles. When...

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#### Launch Altitude Tracker

Using PVC pipe and aquarium tubing, build an altitude tracker. Pupils then use the altitude tracker, along with a tangent table, to calculate the altitude of a launched rocket using the included data collection sheet.

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#### Lighthouse Keeper

Shine a light on the distance between two boats. The short assessment provides the angle of depression from a lighthouse to two boats. The learners represent the situation with a diagram and calculate the distance between the two boats.

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#### Sine and Cosine

What is the complementary relationship between sine and cosine? Using a right triangle, pupils explain why the sine of one acute angle is equal to the cosine of the other. The triangle measurements are given as variables.

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#### Trigonometric Functions

In this trigonometric functions worksheet, students solve and complete 28 various types of problems. First, they convert each function from degrees to radians. Then, students find the six trigonometric functions associated with the x...

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#### Trigonometry Formula Worksheet

In this trigonometry activity, students solve right triangle problems. They find the sine, cosine and tangent of given triangles. This on-line, interactive activity contains 6 problems. Answers are provided.

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#### Algebra Skills Sections 23

In this algebra skills activity, high schoolers solve/simplify 20 short answer problems. Students solve/simplify quadratic, absolute value, exponential, logarithmic, trigonometric, and radical equations/expressions.

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#### Sudoku Puzzle with Limits

In this limit problems worksheet, students solve 28 limits problems. Students find the limits of various functions as x approaches a certain number. Students solve a sudoku puzzle with their answers.

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#### Inverse Trig Functions

In this inverse trig functions activity, students solve and complete 8 different types of problems. First, they find the derivatives of each inverse trig function shown. Then, students find the arc degree of each function.

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#### Trig Identities and Antiderivatives

In this math worksheet, students investigate the use of the trigonometric identities and the antiderivatives. They are asked to memorize the identities.

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#### Trigonometric Identities

Students calculate the six trigonometric identities. In this algebra lesson, students verify other identities using the basic trigonometric identities of sine, cosine and tangent. They complete a worksheet with hints and then are graded...

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#### Derivatives of the 6 Inverse Trig Functions

Student list the 6 trig functions and identify their inverse functions. In this trigonometry lesson, students derive the inverse trig functions using the derivative. They solve problems using the inverse functions through substitution.

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#### Graphing Trig Functions

In this trig learning exercise, learners graph the six trig functions and identify the period of each function. There are 4 questions.

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#### Trig Cut Ups

In this trigonometry worksheet, students rearrange 16 squares to a form one large square in which all of the trig identities match up. There is an answer key.

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#### Trigonometric Graphs

In this trigonometric graphs worksheet, 11th graders solve and complete 16 different problems. First, they determine the period of the given functions. Then, students describe the period, amplitude, and vertical shift of each function....

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#### Exact Trig Values of Special Angles

For this special angles worksheet, students find the value of given trigonometric functions. This four-page worksheet contains 30 problems. Answers are provided on the last two pages.

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#### Sines and Cosines

In this sines and cosines learning exercise, 11th graders solve and complete 14 different types of problems. First, they write the sine and cosine of a point as fractions is simplest form. Then, students find the measure of an angle to...

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#### Test 3: MAT 104 - Trigonometry

In this trigonometry worksheet, students use trigonometric ratios to determine the measures of angles, and the lengths of legs of triangles. Students read story problems, draw models, and write the equations. This one-page worksheet...

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#### Trigonometry Ratios in Right Triangles

In this trigonometry ratios in right triangles worksheet, 10th graders solve 10 different trigonometric ratios that apply to right triangles. First, they define a trigonometric ratio and its three most common ratios, sine, cosine, and...

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#### Sine, Cosine, Tangent

In this sine, cosine, tangent worksheet, students read short statements, draw illustrations of the statement and then use trigonometric ratios to determine the length of the missing side or measurement of an angle. This five-page...

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#### Differentiate Functions

In this function worksheet, students differentiate functions containing trigonometric ratios. This one-page worksheet contains three problems.

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#### Right Triangle Stuff

In this right triangle worksheet, students use trigonometric ratios to find the hypotenuse, right angle, opposite leg and angles. This one-page worksheet contains eight problems. Answers are provided at the bottom of the page.

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#### Number of Solutions for a Triangle

In this solutions for a triangle learning exercise, students use trigonometric ratios to determine the number of triangles that can be constructed with the given sides and angles. This one-page learning exercise contains 22 problems.

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#### Law of Sines

In this Law of Sines learning exercise, students use trigonometric ratios to determine angle measurement and/or the length of the side of a triangle. This one-page learning exercise contains ten trigonometric ratio problems.

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#### Right Triangles

In this right triangle worksheet, students use trigonometric ratios to determine the length of a missing side or a triangle or determine angle measurement. They match the vector with the correct component form of the vector. Students...

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#### Year 10 Trigonometry

In this math worksheet, students complete the graphic organizers while filling in the missing values by using the trigonometric ratios.

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#### Quiz: Angles in Circles - Angles Outside the Circle

In this angles in circles instructional activity, students explore angles outside a circle. Using given trigonometric ratios, they find the missing angle measurement or the length of a line. This one-page instructional activity contains...

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#### Using a Calculator (Sine, Cosine, Tangent)

In this calculator learning exercise, students use a calculator to solve given trigonometric ratios. They determine the sine, cosine and tangent of expressions. This one-page learning exercise contains ten problems.