1. Evaluate Trigonometric Functions of Any Angle
Section 13.3
Evaluate Trigonometric Functions of Any Angle

2. California Standard: Mathematical Analysis 9
California Standard: Mathematical Analysis 9.0 Students compute by hand, the values of the trigonometric functions. 2.0 Students know the definition of sine and cosine as y- and x- coordinates of points on the unit circle.

3. By following instructions, students will be able to:
OBJECTIVE(S):
By following instructions, students will be able to:
Evaluate trigonometric functions of any angle.

4. Recall: Soh-Cah-Toa

5. The Six Trigonometric Functions
Let be an acute angle of a right triangle. Then the six trigonometric functions of the angle are defined as follows.

6. Definitions of Trigonometric Functions of Any Angle
Let be an angle in standard position with (x,y) a point on the terminal side
of and
(x,y) x y r

7. EXAMPLE 1:
Let (-4,3) be a point on the terminal side of an angle θ in standard position. Evaluate the six trigonometric functions of θ. 7

8. Key Concept – The Unit Circle

9. Unit Circle

10. EXAMPLE 2:
Use the unit circle to evaluate the six trigonometric functions of θ=270° 10

11. U-TRY #1: Evaluate the six trigonometric functions of θ.
Use the unit circle to evaluate the six trigonometric functions of θ=180°.

12. Key Concept – Reference Angle Relationships

13. Note: A S T C

14. EXAMPLE 3:
Find the reference angle θ’ for (a)
and (b) 14

15. EXAMPLE 4:
Evaluate (a) and (b) 15

16. U-TRY #2: Sketch the angle. Then find its reference angle. a) b) c) d)
2) Evaluate without using a calculator.

17. EXAMPLE 5: 17

18. EXAMPLE 6: 18

19. Homework
Sec 13.3 WS