Trigonometric Functions of Any Angle (Section 4-4)

1. Trigonometric Functions of Any Angle (Section 4-4)

3. Determine the exact value of the six trigonometric functions of the angle θ. Example 1

4. The point is on the terminal side of an angle in standard position. Determine the exact values of the six trigonometric functions of the angle. Example 2 (2, -3)

6. State the quadrant in which θ lies. Example 3 sin θ > 0 and cosθ < 0

7. State the quadrant in which θ lies. Example 4 sec θ < 0 and tan θ > 0

8. Find the values of the six trigonometric functions of θ. Example 5 θ lines in Quadrant III

9. Find the values of the six trigonometric functions of θ. Example 6

10. The terminal side of θ lies on the given line in the specified quadrant. Find the values of the six trigonometric functions of θ by finding a point on the line. Example 7 Quadrant III

11. Evaluate the trig function of the quadrant angle. Example 8 a) sin π b) c)

13. Find the reference angle θ’ for the special angle θ. Then sketch θ and θ’ in standard position. Example 9 θ = 300°

14. Find the reference angle θ’ for the special angle θ. Then sketch θ and θ’ in standard position. Example 10 θ = -135°

15. Find the reference angle θ’. Then sketch θ and θ’ in standard position. Example 11 θ = 323°

16. Find the reference angle θ’. Then sketch θ and θ’ in standard position. Example 12 θ =2.3

17. HW #17 pg 294- 295 (1- 51 odd)

18. Pg 291

19. Evaluate the sine, cosine, and tangent of the angle without using a calculator. Example 13

20. Evaluate the sine, cosine, and tangent of the angle without using a calculator. Example 14

21. Evaluate the sine, cosine, and tangent of the angle without using a calculator. Example 15

22. Find the indicated trigonometric value in the specified quadrant. Example 16 Function Quadrant Trigonometric Value II cosθ

23. Find the indicated trigonometric value in the specified quadrant. Example 17 Function Quadrant Trigonometric Value III tan θ

24. Use the given value and the trigonometric identities to find the remaining trigonometric functions of the angle. Example 18

25. Use a calculator to evaluate the trigonometric function. (Be sure your calculator is set in the correct angle mode.) Example 19

26. Use a calculator to evaluate the trigonometric function. (Be sure your calculator is set in the correct angle mode.) Example 20

27. Use a calculator to evaluate the trigonometric function. (Be sure your calculator is set in the correct angle mode.) Example 21

28. Find two solutions to the equation. Give your answers in degrees (0< θ < 360) and radians (0< θ < 2). Do not use a calculator. Example 22

29. Find two solutions to the equation. Give your answers in degrees (0< θ < 360) and radians (0< θ < 2). Do not use a calculator. Example 23

30. Find two solutions to the equation. Give your answers in degrees (0< θ < 360) and radians (0< θ < 2). Do not use a calculator. Example 24

31. Find two solutions to the equation. Give your answers in degrees (0< θ < 360) and radians (0< θ < 2). Do not use a calculator. Example 25

32. Find the exact value of each function for the given angle for f(θ) = sin θ and g(θ) = cosθ. Do not use a calculator. Example 26 f(θ) + g(θ) e) 2f(θ) f(θ) – g(θ) f) g(-θ) [g(θ)]2 f(θ) g(θ)

33. HW #18 pg 295 (53 – 107 odd)