Trigonometric functions

• Cosine Function

Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle.

• Simplifying Trigonometric Expressions

Choose the correct steps to simplify a trigonometric function. Use step-by-step feedback to diagnose incorrect steps.

• Sine Function

Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle.

• Sound Beats and Sine Waves

Listen to and see interference patterns produced by sound waves with similar frequencies. Test your ability to distinguish and match sounds as musicians do when they tune their instruments. Calculate the number of "sound beats" you will hear based on the frequency of each sound. [Note: Headphones are recommended for this Gizmo.]

• Sum and Difference Identities for Sine and Cosine

Choose the correct steps to evaluate a trigonometric expression using sum and difference identities. Use step-by-step feedback to diagnose incorrect steps.

• Tangent Function

Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle.

• Translating and Scaling Sine and Cosine Functions - Activity A

Experiment with the graph of a sine or cosine function. Explore how changing the values in the equation can translate or scale the graph of the function.

• Translating and Scaling Sine and Cosine Functions - Activity B

Explore the graph of a sine or cosine function. Vary the terms of the equation and examine how the graph changes. Find the amplitude, period, and frequency of the function.

• Unit Circle

Explore the relationship between the unit circle and the graphs of the sine, cosine, and tangent functions.