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...

Build a solid understanding of trigonometric transformations through exploration. Learners work in teams to analyze the effects of different algebraic components on the graph of a sine function. 

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...

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...

Transform your lesson on transformations. Scholars investigate transformations, with particular emphasis on translations and dilations of the graphs of logarithmic and exponential functions. As part of this investigation, they examine...

Use the graphs of the trigonometric functions to set the stage to inverse functions. The lesson reviews the graphs of the basic trigonometric functions and their transformations. Pupils use their knowledge of graphing functions to model...

How does a change in amplitude or period affect the equation of a sine function? Scholars move sliders to change the frequency and period of the sine function. The interactive displays the resulting equation, and pupils determine the...

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...

Learn how to slide sine back and forth and up and down. Pupils move the starting point of a graph of sine vertically and horizontally. They investigate the changes to the equation of the graph in relationship to the translation. They...

Scholars manipulate the amplitude of the graphs of sine and cosine, notice how the change in amplitude is reflected in their graphs, and answer several questions about the concept they noticed.

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...

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. 

Your learners will appreciate having this color-coded set of the six trigonometric functions all on one page. Included are the graphs for sine, cosine, tangent, cosecant, secant, and cotangent. Notice that part of each graph is...

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...

Double win with a comprehensive learning exercise and an excellent worked out answer key. The learning exercise itself is twelve pages and begins with the simple sine and cosine graphs, then, develops into the reciprocal trig...

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...

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...

What effect does changing a parameter have on the graph of a trigonometric function? Pupils use a Desmos applet to explore the general sine graph. They experiment changing different parameters and record the resulting change of the...

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.

Young scholars explore the concept of sine and cosine.  In this sine and cosine lesson, students work in groups to graph sine and cosine functions.  Young scholars examine how coefficients in various parts of each parent...

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.

Polar opposites might not work together—but polar coordinates do! The interactive provides learners the opportunity to graph trigonometric and algebraic functions using polar coordinates. The program takes either individual data points...

Don't give your classes the third degree. Use radians instead! While working with degrees, learners find that they are not efficient and explore radians as an alternative. They convert between the two measures and use radians with the...

It's a sign! Scholars analyze sine functions for patterns in their periods. The exploration advances beyond a simple function to the combination of two functions with even and odd coefficients. Their goal is to find a pattern between the...