1. Trigonometric Functions of Any Angle
Section 4.4
Trigonometric Functions of Any Angle

2. Objective By following instructions students will be able to:
evaluate trigonometric functions of any angle.
use reference angles to evaluate trigonometric functions.
evaluate trigonometric functions of real numbers.

3. Trigonometric Functions of Real Numbers
Standard Angle
Reference Angle
(x,y) x y
opp
adj
r=hyp

4. Example 1: Evaluating Trigonometric Functions
Let (-3,4) be a point on the terminal side of Find the sine, cosine, and tangent of
(-3,4) r

5. Note: A S T C

6. Example 2: Evaluating Trigonometric Functions
Given and , find and

7. Example 3: Trigonometric Functions of Quadrant Angles
Evaluate the sine and cosine functions at the four quadrant angles 0, , , and

8. Example 4: Find the reference angle
a) b) c)

9. Example 5: Trigonometric Functions of Nonacute Angles
Evaluate the trigonometric functions. a) b) c)

10. Example 6: Use Trigonometric Identities
Let be an angle in Quadrant II such that . Find the following using trigonometric identities. a) b)

11. Example 7: Using a Calculator
Use a calculator to evaluate and
Use a calculator to solve

12. Revisit Objective Did we…
evaluate trigonometric functions of any angle?
use reference angles to evaluate trigonometric functions?
evaluate trigonometric functions of real numbers?

13. Homework
Pg 320 #1-105 ALL