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In P 25. sin 20° cos 10° + cos 20° sin 10° 27. cos 70° cos 20° - sin 70° sin 20° tan 20° + tan 25° 29 1- tan 20° tan 25° 77 31. sin COs 12 cos sin 12 12

In P 25. sin 20° cos 10° + cos 20° sin 10° 27. cos 70° cos 20° - sin 70° sin 20° tan 20° + tan 25° 29 1- tan 20° tan 25° 77 31. sin COs 12 cos sin 12 12

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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In Problems 13-24, find the exact value of each expression. In Problems 25-34, find the exact value of each expression. Skill Building TT 14. sin 105° 15. tan 15° 18. sin 12 \3 cos 165° 16. tan 195° 17. sin 12 7T \ 19. cos 12 20. tan 12 17 21. sin 197 22. tan 12 24. cot 12 23. sec 12 15. sin 20° cos 10° + cos 20° sin 10° 26. sin 20° cos 80° - cos 20° sin 80° \ 27. cos 70° cos 20° - sin 70° sin 20° 28. cos 40° cos 10° + sin 40° sin 10 tan 20° + tan 25° 29. 1- tan 20° tan 25° tan 40° - tan 10° 30. 1 + tan 40° tan 10° 77 5m 32. cos cs 12 - cos \31. sin 12 cos 12 sin 12 12 - sin sin 12 12 12 5m 5m cos 18 + sin sin 34. sin 18 33. cos 12 COS 12 12 12 + cos sin 18 18 le Problems 35–40, find the exact value of each of the following under the given conditions: (a) sin (a + B) (b) cos (a + B) (c) sin (a - B) (d) tan (a - B) 2V5 cos B = V5 36. cos a = 5 4 응0<a<플 sing= \ 35. sin a = 0 < a < <B<0 2 5' 4 7 " <a < T; cos B = 1 3T 1 ,T<B< 37. tan a = - 3 2 38. tan a = T < a < 12 sin B = 5 39. sin a = 13 1 40. cos a = < a < -T; tan B = - <B < T < a < 0; sin B = 2 1 ,0 in quadrant II, find the exact value of: 1 O in quadrant IV, find the exact value of: 41. If sin 0 = 42. If cos e = 4 (a) cos 0 (a) sin 0 (b) (b) sinj 0 - (c) cosl 0 - (c) cos (d) tan +1 (d) tan 0 -- In Problems 43–48, use the figures to evaluate each function if f (x) = sin x, g (x) = cos x, and h (x) = tan x. 43. f(a + B) 44. g (α + β) y 45. g(a - B) x2 + y2 = 4 x2 + y2 = 1 46. f(α-β) (x, 1) 47. h(a + B) 48. h (α -β) In Problems 49-74, establish each identity. 49. sin + 6 = cos 0 50. cos +0 = -sin 0 51. sin (7 – 0) = sin 0 52. cos (7 - A) = - cos 0 53. sin (T + 0) = -sin 0 54. cos (7 + 0) = -cos 0 55. tan (7 - 0) = - tan 0 56. tan (27 - 0) = -tan 0 57. sin 3m 58. cos = - cos 0 = sin 0 59. sin (a + B) + sin(a – B) = 2 sin a cos ß
Transcribed Image Text:In Problems 13-24, find the exact value of each expression. In Problems 25-34, find the exact value of each expression. Skill Building TT 14. sin 105° 15. tan 15° 18. sin 12 \3 cos 165° 16. tan 195° 17. sin 12 7T \ 19. cos 12 20. tan 12 17 21. sin 197 22. tan 12 24. cot 12 23. sec 12 15. sin 20° cos 10° + cos 20° sin 10° 26. sin 20° cos 80° - cos 20° sin 80° \ 27. cos 70° cos 20° - sin 70° sin 20° 28. cos 40° cos 10° + sin 40° sin 10 tan 20° + tan 25° 29. 1- tan 20° tan 25° tan 40° - tan 10° 30. 1 + tan 40° tan 10° 77 5m 32. cos cs 12 - cos \31. sin 12 cos 12 sin 12 12 - sin sin 12 12 12 5m 5m cos 18 + sin sin 34. sin 18 33. cos 12 COS 12 12 12 + cos sin 18 18 le Problems 35–40, find the exact value of each of the following under the given conditions: (a) sin (a + B) (b) cos (a + B) (c) sin (a - B) (d) tan (a - B) 2V5 cos B = V5 36. cos a = 5 4 응0<a<플 sing= \ 35. sin a = 0 < a < <B<0 2 5' 4 7 " <a < T; cos B = 1 3T 1 ,T<B< 37. tan a = - 3 2 38. tan a = T < a < 12 sin B = 5 39. sin a = 13 1 40. cos a = < a < -T; tan B = - <B < T < a < 0; sin B = 2 1 ,0 in quadrant II, find the exact value of: 1 O in quadrant IV, find the exact value of: 41. If sin 0 = 42. If cos e = 4 (a) cos 0 (a) sin 0 (b) (b) sinj 0 - (c) cosl 0 - (c) cos (d) tan +1 (d) tan 0 -- In Problems 43–48, use the figures to evaluate each function if f (x) = sin x, g (x) = cos x, and h (x) = tan x. 43. f(a + B) 44. g (α + β) y 45. g(a - B) x2 + y2 = 4 x2 + y2 = 1 46. f(α-β) (x, 1) 47. h(a + B) 48. h (α -β) In Problems 49-74, establish each identity. 49. sin + 6 = cos 0 50. cos +0 = -sin 0 51. sin (7 – 0) = sin 0 52. cos (7 - A) = - cos 0 53. sin (T + 0) = -sin 0 54. cos (7 + 0) = -cos 0 55. tan (7 - 0) = - tan 0 56. tan (27 - 0) = -tan 0 57. sin 3m 58. cos = - cos 0 = sin 0 59. sin (a + B) + sin(a – B) = 2 sin a cos ß
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