IM Alg2.6.9 Lesson: Introduction to Trigonometric Functions

Suppose there is a point on the unit circle at . Describe how the -coordinate of changes as it rotates once counterclockwise around the circle.

Describe how the -coordinate of changes as it rotates once counterclockwise around the circle.

Use the class display, the table from a previous lesson, or the applet to estimate the value of and where is the measure of an angle in radians.

Use technology to plot the values of y=cos(θ), where θ is the measure of an angle in radians.

What do you notice about the two graphs?

Explain why any angle measure between 0 and gives a point on each graph.

Could these graphs represent functions? Explain your reasoning.

Looking at the graphs of and , at what values of do ?

Where on the unit circle do these points correspond to?

For each of these equations, first predict what the graph looks like, and then check your prediction using the applet at the end of the activity.

To enter the symbol for

, use the onscreen keyboard which can be accessed through the keyboard

icon. You should enter each equation as a function. For example,

can be entered as

. Some examples are given in the applet below.

For the equation given, predict what the graph looks like, and then check your prediction using technology: .