7-4 Evaluating and Graphing Sine and CosineObjectives:1. Use reference angles and special angles

to evaluate sine and cosine functions2. Graph sine and cosine functions.

The reference angle for any angle θ is:

the positive acute angle formed by the terminal ray of θ and the x-axis.

Reference Angles

We can evaluate any trig function for any angle by using its reference angle.

Determine the sign by quadrant. Remember: “All Students Take Calculus!”

Using Reference Angles

Express sin 695° in terms of a reference angle.

Example 1

Express cos 200° in terms of a reference angle.

You Try!

The “Hand Trick”

Evaluate each without looking at the unit circle. (Use the reference angle!)

Examples

Evaluate each without looking at the unit circle.

You Try!

Graphing Sine Functions

θ sin θ0

π/4π/2

3π/4π

1

-1

Graphing Cosine Functions

θ cos θ0

π/4π/2

3π/4π

1

-1