EngageNY
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...
EngageNY
Piecewise Functions
Show your class members that if they can graph a linear function, they can graph an absolute value function. Groups create an absolute value graph using a table, then entertain the idea of an absolute value function defined as two...
Mathematics Vision Project
Module 6: Trigonometric Functions
Create trigonometric functions from circles. The first lesson of the module begins by finding coordinates along a circular path created by a Ferris Wheel. As the lessons progress, pupils graph trigonometric functions and relate them to...
EngageNY
From Circle-ometry to Trigonometry
Can you use triangles to create a circle? Learners develop the unit circle using right triangle trigonometry. They then use the unit circle to evaluate common sine and cosine values.
Concord Consortium
Functions by the Slice
Piece by piece ... dismantling a function can highlight interesting patterns. The task asks learners to slice functions in sections with the same vertical change. They then recreate the graph with these slices positioned horizontally....
CK-12 Foundation
Algebraic Functions: Vertical Line Test
To be (a function) or not to be (a function). An easy-to-use interactive has pupils drag a vertical line onto several graphs to determine if they represent functions. Some challenge questions assess understanding of this idea.
Mt. San Antonio Collage
Quiz 1: Types of Functions
Sometimes the best things are already done for you! Here is a six-problem quiz that has a variety of problems ranging from solving quadratic equations to interpreting a function. The piece-de-resistance is the worked out answer key in...
CK-12 Foundation
Domain, Range, and Signs of Trigonometric Functions: Sine and Cosine
Is there a relationship between the sign of sine and cosine and the angle on the unit circle? Scholars use an interactive to see the value of sine and cosine within different quadrants. they then use the information to determine the...
CK-12 Foundation
Unit Circle: Medieval Castle Defense
Who needs a plan — let trigonometry protect you! Pupils determine the angle of an approaching enemy to a village wall. The scholars determine the exact value of trigonometric functions for the angle. Class members use trigonometry to...
CK-12 Foundation
Trigonometric Functions of Negative Angles
When is the trigonometric value of a negative angle the same as the positive angle? Pupils compare the values of trigonometric functions for different angles and their negatives. The interactive resource provides a visual display to make...
EngageNY
Secant and the Co-Functions
Turn your class upside down as they explore the reciprocal functions. Scholars use the unit circle to develop the definition of the secant and cosecant functions. They analyze the domain, range, and end behavior of each function.
EngageNY
Graphing the Sine and Cosine Functions
Doing is more effective than watching. Learners use spaghetti to discover the relationship between the unit circle and the graph of the sine and cosine functions. As they measure lengths on the unit circle and transfer them to a...
University of North Texas
Library of Functions
Join the family picnic and see how all the functions come together in a PowerPoint that highlights their main features. As it includes topics such as domain, range, and intercepts, the slides are a great guide to promote class...
EngageNY
Ferris Wheels—Using Trigonometric Functions to Model Cyclical Behavior
Have class members going in circles as they model the path of a Ferris Wheel using trigonometric functions. Building on the previous lesson in this series on transformations, learners use trigonometric functions to model wheels of...
Concord Consortium
Measuring the Unit Circle
Here's the right task to investigate right triangles in the unit circle. A short performance task has learners determine the product of two side lengths in a unit circle. They must apply similarity concepts and trigonometric ratios to...
EngageNY
Comparing Quadratic, Square Root, and Cube Root Functions Represented in Different Ways
Need a real scenario to compare functions? This activity has it all! Through application, individuals model using different types of functions. They analyze each in terms of the context using the key features of the graphs.
CK-12 Foundation
Trigonometric Functions and Angles of Rotation: The Triangle in the Circle
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...
EngageNY
The Height and Co-Height Functions of a Ferris Wheel
Show learners the power of mathematics as they model real-life designs. Pupils graph a periodic function by comparing the degree of rotation to the height of a ferris wheel.
Flipped Math
Unit Circle and Radians
Measure angles is easy as pi. Pupils review special right triangles to find exact values for trigonometric functions. Scholars learn about radians and how they connect to measurements in degrees. They find exact and approximate values of...
CK-12 Foundation
Reference Angles and Angles in the Unit Circle: Exploring Reference Angles
A steal of a deal — get four angles for the value of one. An interactive resource allows individuals to visualize all four angles that have the same reference angle. Pupils answer questions by using the interactive to create the...
CK-12 Foundation
Trigonometric Functions of Angles Greater than 360 Degrees: Snowboarding
Spin through the trigonometric functions. Scholars determine the angle of rotation a snowboarding snowman makes at various distances in his jump. The class members then calculate the values of trigonometric functions for those angles.
CK-12 Foundation
Six Trigonometric Functions and Radians: Degrees to Radians and Back Again!
How do degrees relate to radians? The interactive allows pupils to manipulate the size of an angle in a unit circle to help see that relationship. Users determine the radian measure for given degree measures of angles, realizing the...
Curated OER
Graphs
In this graphs worksheet, students solve and complete 15 various types of problems. First, they determine the range of the function of the graph shown and write in interval notation. Then, students find the domain of the function in the...
EngageNY
Why Call It Tangent?
Discover the relationship between tangent lines and the tangent function. Class members develop the idea of the tangent function using the unit circle. They create tables of values and explore the domain, range, and end behavior of...