Interactive
CK-12 Foundation

Reciprocal Identities

For Students 10th - 12th Standards
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...
Interactive
CK-12 Foundation

Basic Trigonometric Functions: Ladder Length

For Students 9th - 12th Standards
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...
Interactive
PHET

Trig Tour

For Students 9th - 12th Standards
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...
Interactive
Curated OER

Connect The Dots Trig. Identities

For Students 10th - 11th
In this trig. identities worksheet, students connect the dots to equivalent values.  Then students find the isosceles right triangle formed.  Solutions are provided.
Interactive
CK-12 Foundation

Double Angle Identities: Ferris Wheel

For Students 10th - 12th
Use a Ferris wheel to soar to new heights of understanding on double angle identities. Here is an interactive that applies an example of a Ferris wheel to show how doubling the angle does not double the value of a trigonometric ratio....
Interactive
CK-12 Foundation

Derivatives of Trigonometric Functions: Derivative of sin(x)

For Students 11th - Higher Ed
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...
Interactive
CK-12 Foundation

Trigonometric Functions and Angles of Rotation: The Triangle in the Circle

For Students 10th - 12th Standards
Go around the unit circle and create triangles. Pupils move a point around the unit circles to visualize the triangle associated with the angle in standard position. The three main trigonometric functions are defined in terms of the legs...
Interactive
CK-12 Foundation

Fundamental Trigonometric Identities: Tangent Identity

For Students 10th - 12th
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.
Interactive
CK-12 Foundation

Pythagorean Theorem for Solving Right Triangles: Solving the Triangle

For Students 9th - 12th Standards
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...
Interactive
CK-12 Foundation

Length of a Chord: Distance Across a Ferris Wheel

For Students 9th - 12th Standards
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.
Interactive
CK-12 Foundation

Finding Exact Trigonometric Values Using Double Angle Identities: Trig Values Using Double and Half Angle Formulas

For Students 10th - 12th
The more you know, the more you can learn. Scholars apply the double angle and half angle formulas to determine trig values based on known values. They use an interactive that provides sine and cosine values to aid calculations.
Interactive
Curated OER

Inverse Trig Functions: Chain Rule

For Students 9th - Higher Ed
In this trigonometric functions worksheet, students differentiate inverse trigonometric functions using the chain rule. There are 15 questions.
Interactive
Curated OER

Integration of Trigonometric Integrals

For Students 9th - 10th
In this trigonometry activity, students use integration to solve for the six different trigonometric identities. They use indefinite integrals to solve problems. There are 27 questions with an answer key.
Interactive
CK-12 Foundation

Horizontal Translations or Phase Shifts: Sine

For Students 10th - 12th Standards
Shift a trigonometric function and find its new equation. Pupils translate a sine function on a graph. The scholars determine the equation of the function that represents the translated graph and observe the connection between a...
Interactive
Curated OER

Inverse Trigonometric Functions-Using a Calculator

For Students 10th
In this geometry learning exercise, 10th graders use a calculator to evaluate the inverse of a trigonometric function. The one page interactive learning exercise contains ten questions. Answers and hints are included. 
Interactive
CK-12 Foundation

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

For Students 9th - 12th Standards
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...
Interactive
CK-12 Foundation

Sine, Cosine, and Tangent Functions: Lighthouse

For Students 9th - 12th Standards
How far is that boat from the lighthouse? Scholars create diagrams to represent a scenario given the angle of depreciation from a lighthouse to a boat. Learners apply the basic trigonometric functions to find various distances...
Interactive
Curated OER

Trigonometry Formula Worksheet

For Students 10th - 12th
In this trigonometry worksheet, students solve right triangle problems.  They find the sine, cosine and tangent of given triangles.  This on-line, interactive worksheet contains 6 problems.  Answers are provided.
Interactive
Curated OER

True or False Algebraic Statements

For Students 11th - Higher Ed
In this algebraic statements worksheet, students determine whether thirty-three algebraic equations are true of false statements. A math cartoon as well as a link to the solutions is provided at the end of the worksheet.
Interactive
CK-12 Foundation

Horizontal Translations or Phase Shifts: Tangent

For Students 10th - 12th Standards
Patterns can be shifty! Find the pattern when shifting the graph of tangent. Pupils move the graph of tangent to different locations on the coordinate plane. They observe what happens to the function and its vertical asymptotes...
Interactive
CK-12 Foundation

Vertical Translations: Vertical Shift of Sinusoidal Functions

For Students 10th - 12th Standards
Create a shift in TV viewing habits. The interactive presents a cosine model of an individual's TV viewing habits during a year. Class members move the model to reflect given conditions. Finally, they determine key features from the...
Interactive
Curated OER

Differentiation of Trigonometry Functions

For Students 9th - 11th
In this trigonometry instructional activity, students differentiate the different trigonometric identities. They derive the sine, cosine, tangent and inverses of these trig identities. There are 18 questions with an answer key.
Interactive
Curated OER

Graph a csc Trigonometric Function

For Students 11th - Higher Ed
In this trigonometry function activity, students graph one csc function with transformations.  A grid for graphing is provided. 
Interactive
CK-12 Foundation

Angles of Elevation and Depression: Fly-By Calibration

For Students 9th - 12th Standards
Determine the distance between two trees from afar. Pupils use an interactive resource to create two right triangles using trees and a plane. They determine the horizontal legs of each triangle to find the distance between the two trees.

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