1. 4.4 Trigonmetric functions of Any Angle

2. Objective Evaluate trigonometric functions of any angle Use reference angles to evaluate trig functions

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

4. The cosecant function is the reciprocal of the sine. The secant function is the reciprocal of the cosine. The cotangent function is the reciprocal of the tangent function.

5. Example 1 Let (-3, 4) be a point on the terminal side of θ. Find the sine, cosine, and tangent of θ.

6. Example 2 Let (2, 5) be a point on the terminal side of θ. Find the sine, cosine, and tangent of θ.

7. Signs of the Trigonometric Functions

8. Signs of the Trig Functions A means that all trig. functions are positive. S means that all sine and cosecant functions are positive. T means that all tangent and cotangent functions are positive. C means that all cosine and secant functions are positive.

9. Example 3 State whether each value is positive, negative, or zero. a) cos 75° positive b)sin 3π 0 c)cos 5π negative d)sin(-3π) 0

10. Example 4 Given.

11. Example 5 Angle θ is in standard position with its terminal side in the third quadrant. Find the exact value of cos θ if

12. Example 6 Angle θ is in standard position with its terminal side in the fourth quadrant. Find the exact value of sin θ if

13. Reference Angles Definition Let θ be an angle in standard position. Its reference angle is the acute angle θ’ formed by the terminal side of θ and the horizontal axis.

14. Reference angles

15. Example 7 Finding reference angles.

16. Trigonometric Values of Common Angles

18. Example 8 Use the reference angle to find sin θ, cos θ, and tan θ for each value of

19. Example 9 Determine the values of θ for which

20. If the value of one of the trig functions of any angle is known, a calculator can be used to determine the angles having that value.

21. Example 10 Find values of θ, where to the nearest tenth of a degree.

22. Example 11 Find values of θ, where To the nearest hundredth of a radian.