8. A function fis Section 4.2 Trigonometric Functions Defined on the Unit Clerce 477 9. The period of the tangent and cotangent functions is. if fur+p) = f() for some constant p. secant functions is 10. The cosine function is an function because sin(-1)=-sint. The period of the sine, cosine, cosecant, and For Exercises 11-14, determine if the point lies on the unit circle. Objective 1: Evaluate Trigonometric Functions Using the Unit Circle function because cos(-1)=cost. The sine function is an. 11. V61 12. (VTO VTS) 13. (-V7-223) 10 14. (-2V34 3V17) For Exercises 15-18, the real number t corresponds to the point P on the unit circle. Evaluate the six trigonometric functions of t. (See Example 1) 15. y 1 P(-) 16. 17. y x + y = 1 P(-) x y 19. Fill in the ordered pairs on the unit circle corresponding to each real number f. ) t= = (---) (---) (----) = 18. 1 For Exercises 20-23, identify the coordinates of point P. Then evaluate the six trigonometric functions of t. (See Example 2) 20. P(x, y) y 1= ST 6 21. P(x, y) y 22. 4 t=- P(x, y) t= 23. For Exercises 24-26, identify the ordered pairs on the unit circle corresponding to each real number t. 2T 24. a. t = 3 7T 25. a. t = 6 5 26. a. t = 3 5T b. t = 4 3 b. t = -- 4 b. t = 7 4 5 ps to C. t == 6 4 c. t = 3 C. t = -- 6 For Exercises 27-32, evaluate the trigonometric function at the given real number. y P(x,y) 11T 2T 5 27. f(t) = cost; t = 28. g(t) = sint; t = 29. h(t)=cott; t = 4 3 7 30. s(t) = sect; t = 5 3 31. z(t) = csct; t = 32. r(t) = tant; t = 6 4 7T ID 12