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= tan x. bns znoitsailggA 1oolems 43-48, use the figures to evaluate each function if f (x) = sin x, g(x) = cos x, and h(x) 43. f(a + B) In Problems 49-74, estahlish each identity. yt x2 + y2 = 1 44. g(α + β) x2 + y2 = 4 (x, 1) 45. g(a - B) 46. f(a - B) 47. h(a + B) 48. h (α- β) 1/3

= tan x. bns znoitsailggA 1oolems 43-48, use the figures to evaluate each function if f (x) = sin x, g(x) = cos x, and h(x) 43. f(a + B) In Problems 49-74, estahlish each identity. yt x2 + y2 = 1 44. g(α + β) x2 + y2 = 4 (x, 1) 45. g(a - B) 46. f(a - B) 47. h(a + B) 48. h (α- β) 1/3

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.2: Trigonometric Functions Of Angles
Problem 18E
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Problems 13-24, find the exact value of each expression. n Problems 25–34, find the exact value of each expression. 9. sin + 0 In Problems 35-40, find the exact value of each of the following under the given conditions: SECTION 7.5 Sum and Difference Formulas 497 Skill Building 14. sin 105° 15. tan 15° (12) | Li cos 165° 16. tan 195° 57 17. sin 20. tan 12 17 21. sin 18. sin 12 12 | 19, cos 12 12 19 22. tan -1, and 12 23. sec 24. cot 26. sin 20° cos 80° cos 20° sin 80 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° plutions 7TT sin 12 - cos cos 12 12 5m \ 3l. sin 12 7m COS 12 32. cos 77 sin 12 - sin 12 12 57 + sin 12 sin 12 cos 57 sin 18 33. cos 12 12 34. sin 18 cos 18 + cos 18 (a) sin (a + B) (b) cos (a + B) (c) sin(a - B) (d) tan (a - B) 2V5 5 <B<0 3 < cos ß = V5 0 < a \35 sin a ==,0 < a < 36. cos a = 4. i sin B = - <B<0 4 T <a < m; cos ß = 5,0 < B < 1 sin B = 2 37 <B < 37. tan a = 3 2 38. tan a = T< a < 12 2' 37 < a < -T; tan B = - 2 5 39. sin a = 13' V3. < B < = 1 40. cos a = 2 <a<0; sin B = 2 <B < 1 0 in quadrant II, find the exact value of: 1 0 in quadrant IV, find the exact value of: 4' 41. If sin 0 = 42. If cos 0 = 3' (a) cos 0 (a) sin 0 (b) sin(0 -) of two (b) sin 0 + een the (c) cos e - (c) cos e + le that 20 (d) tan e - (d) tan e + 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. bns znoitsailggA y wod e 43. f(a + B) 44. g(α + β) x2 + y2 = 1 x2 + y2 = 4 (x, 1) ad 45. g(a – B) 46. f(a – B)ulo (d) 47. h (a + B) 48. h (α β) es the Problems 49-74, establish each identity. s ta od 51. sin (7 - 0) = sin 0 hole = - sin 0 50. cos = cos A 54. cos ( 7 + 0) = -cos 0 52. cos (7 - 0) 3m 57. sin 53. sin (7 + 0) = -sin 0 = - cos 0 = - cos e 35. tan (7 - 0) = -tan 0 0) = -tan 0 56. tan (27 ent to (3m 58. cos )nia (u + 0 59. sin (a + B) + sin (æ – B) = 2 sin a cos B = sin 0 d borzodiN
Transcribed Image Text:Problems 13-24, find the exact value of each expression. n Problems 25–34, find the exact value of each expression. 9. sin + 0 In Problems 35-40, find the exact value of each of the following under the given conditions: SECTION 7.5 Sum and Difference Formulas 497 Skill Building 14. sin 105° 15. tan 15° (12) | Li cos 165° 16. tan 195° 57 17. sin 20. tan 12 17 21. sin 18. sin 12 12 | 19, cos 12 12 19 22. tan -1, and 12 23. sec 24. cot 26. sin 20° cos 80° cos 20° sin 80 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° plutions 7TT sin 12 - cos cos 12 12 5m \ 3l. sin 12 7m COS 12 32. cos 77 sin 12 - sin 12 12 57 + sin 12 sin 12 cos 57 sin 18 33. cos 12 12 34. sin 18 cos 18 + cos 18 (a) sin (a + B) (b) cos (a + B) (c) sin(a - B) (d) tan (a - B) 2V5 5 <B<0 3 < cos ß = V5 0 < a \35 sin a ==,0 < a < 36. cos a = 4. i sin B = - <B<0 4 T <a < m; cos ß = 5,0 < B < 1 sin B = 2 37 <B < 37. tan a = 3 2 38. tan a = T< a < 12 2' 37 < a < -T; tan B = - 2 5 39. sin a = 13' V3. < B < = 1 40. cos a = 2 <a<0; sin B = 2 <B < 1 0 in quadrant II, find the exact value of: 1 0 in quadrant IV, find the exact value of: 4' 41. If sin 0 = 42. If cos 0 = 3' (a) cos 0 (a) sin 0 (b) sin(0 -) of two (b) sin 0 + een the (c) cos e - (c) cos e + le that 20 (d) tan e - (d) tan e + 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. bns znoitsailggA y wod e 43. f(a + B) 44. g(α + β) x2 + y2 = 1 x2 + y2 = 4 (x, 1) ad 45. g(a – B) 46. f(a – B)ulo (d) 47. h (a + B) 48. h (α β) es the Problems 49-74, establish each identity. s ta od 51. sin (7 - 0) = sin 0 hole = - sin 0 50. cos = cos A 54. cos ( 7 + 0) = -cos 0 52. cos (7 - 0) 3m 57. sin 53. sin (7 + 0) = -sin 0 = - cos 0 = - cos e 35. tan (7 - 0) = -tan 0 0) = -tan 0 56. tan (27 ent to (3m 58. cos )nia (u + 0 59. sin (a + B) + sin (æ – B) = 2 sin a cos B = sin 0 d borzodiN
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