Lesson 9 – Graphs of the Primary Trigonometric Functions

Learning Goals:

• Use radians to graph the primary trigonometric functions.

The Unit Circle

The unit circle is a circle that is centered at the origin and has a radius of 1 unit. On the unit circle, the sine and cosine functions take a particularly simple form:

The value of  is the y-coordinate of each point on the circle , and the value of is the x-coordinate. As a result, each point on the circle can be represented by the ordered pair:

(x, y) = ()

Where  is the angle formed between the positive x-axis and the terminal arm of the angle that passes through each point.

For example the point  lies on the terminal arm of the angle .

Evaluating each trigonometric expression using the special triangles results in the ordered pair .

Repeating this process for other angles between 0 and 2π results in the following diagram:

Success Criteria:

I am able to

• Use radians to graph the primary trigonometric functions.