764 CHAPTER 7 Trigonometric Identities and Equations Chapter 7 Review Exercises Concept Check For each expression in Column I, choose the expression from Column II that completes an identity. I 1. sec x = _____ 2. csc x = _____ 3. tan x = _____ 4. cot x = _____ 5. tan2 x = _____ 6. sec2 x = _____ II A. 1 sin x B. 1 cos x C. sin x cos x D. 1 cot2 x E. 1 cos2 x F. cos x sin x Use identities to write each expression in terms of sin u and cos u, and then simplify so that no quotients appear and all functions are of u only. 7. sec2 u - tan2 u 8. cot 1-u2 sec 1-u2 9. tan2 u11 + cot2 u2 10. csc u - sin u 11. tan u - sec u csc u 12. csc2 u + sec2 u Work each problem. 13. Use the trigonometric identities to find sin x, tan x, and cot1-x2, given cos x = 3 5 and x in quadrant IV. 14. Given tan x = - 5 4 , where p 2 6x 6p, use the trigonometric identities to find cot x, csc x, and sec x. 15. Find the exact values of the six trigonometric functions of 165°. 16. Find the exact values of sin x, cos x, and tan x, for x = p 12 , using (a) difference identities (b) half-angle identities. Concept Check For each expression in Column I, use an identity to choose an expression from Column II with the same value. Choices may be used once, more than once, or not at all. I 17. cos 210° 18. sin 35° 19. tan1-35°2 20. -sin 35° 21. cos 35° 22. cos 75° 23. sin 75° 24. sin 300° 25. cos 300° 26. cos1-55°2 II A. sin1-35°2 B. cos 55° C. B1 + cos 150° 2 D. 2 sin 150° cos 150° E. cot1-35°2 F. cos2 150° - sin2 150° G. cos1-35°2 H. cot 125° I. cos 150° cos 60° - sin 150° sin 60° J. sin 15° cos 60° + cos 15° sin 60° Use the given information to find sin1x + y2, cos1x - y2, tan1x + y2, and the quadrant of x + y. 27. sin x = - 3 5 , cos y = - 7 25 , x and y in quadrant III 28. sin x = 3 5 , cos y = 24 25 , x in quadrant I, y in quadrant IV 29. sin x = - 1 2 , cos y = - 2 5 , x and y in quadrant III 30. sin y = - 2 3 , cos x = - 1 5 , x in quadrant II, y in quadrant III
RkJQdWJsaXNoZXIy NjM5ODQ=