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0 >0 11. tan 0 = 3° 2 12. tan 0 = 2° > e > 0 9A 3' 2 13. cos 0 = - -> 0 > 4 > 0 > u V3 37 14. sin 0 = 15. sec 0 = 3, L > 0>- sin 0 > 0 2 16. csc 0 = -V5, cos 0 < 0=""><0>< 27="" 18.="" sec="" 0="2," 17.="" cot="" 0="" -2,="" 0=""> 0 ɔəs 0 > e uIS In Problems 21-30, use Half-angle Formulas to find the exact value of each expression. 0 > 0 ɔsɔ 'c- = A uei "61 20. cot 0 = 3, 0 > e soɔ \ 21. sin 22.5° 22. cos 22.5° 23. tan 8 157 24. tan 25. cos 165° 8 26. sin 195° 27. sec 8 29. sin 8 30. cos In Problems 31–42, f(x) = sin x, g (x) = cos x, and h(x) = tan x. Use the figures below to evaluate each function. 31. f(20) 32. g(20) 33. (x, 2) x2 + y2 = 5 x2 + y2 = 1 34. f 35. h(20) y *9E ybb 37. 8(2a) 38. f(2a) n offT (a) 39. 40. g 41. h 42. h(2a) () btained as.t 43. Show that sin* 0 = 3 cos (20) + cos (40). 44. Show that sin ( 40) = (cos 0) (4 sin 0 – 8 sin 0). A 45. Show that sin? 0 cos 0 1. 1. cos ( 40). A 46. Show that sin* 0 cos“ 0 = 128 3. cos (40) + 32 cos ( 80). 48. Find an expression for cos (46) as a fourth-degree polynomial 128 8. in thn expression for cos (30) as a third-degree polynomial the variable cos 0. in the variable cos 0. 50. Find an expression for cos (50) as a fifth-degree polynomial in the variable cos 0. In the variable sin 0. 7.6 Assess Your Understanding 49. Find an expression for sin (50) as a fifth-degree polynomial ాయ parts fa) d 30 "/>
Extracted text: SECTION 7.6 Double-angle and Half-angle Formulas 507 concepts and Vocabulary 0soɔ = (07) s03 e soɔ - I 2 7. Multiple Choice Choose the expression that completes the Half-angle Formula for cosine functions: cos- 2. sin %3D 2. 1+ cos a ) so) - I 2. cos a- sin a e soɔ - I + (B) 3. tan 2 I (9) 2 tan 0 cos a 4. True or False tan (20) I (3) tan? 0 + (P) s True or False sin ( 20) has two equivalent forms: D soɔ + I 8. Multiple Choice If sin a = ± 2 sin 0 cos 0 statement describes how 0 is related to a? then which 6. True or False tan ( 20) + tan (20) = tan (40) 0 „soɔ - 0 „UỊS pun Problems 9-20, use the information given about the angle 0,0 s 0 < 27,="" to="" find="" the="" exact="" value="" of:="" సబ="" 0="e" (b)="" 30="" (q)="" skill="" building="" 0="0" (p)="" 07="0" ()="" (a)="" sin="" (20)="" (b)="" cos="" (20)="" cuis="" (2)="" soɔ="" (p)="e" uis="" 6="" 5="" *="" 3.="e" soɔ="" "0i="" 5.="" ,="">0 >0 11. tan 0 = 3° 2 12. tan 0 = 2° > e > 0 9A 3' 2 13. cos 0 = - -> 0 > 4 > 0 > u V3 37 14. sin 0 = 15. sec 0 = 3, L > 0>- sin 0 > 0 2 16. csc 0 = -V5, cos 0 < 0=""><0>< 27="" 18.="" sec="" 0="2," 17.="" cot="" 0="" -2,="" 0=""> 0 ɔəs 0 > e uIS In Problems 21-30, use Half-angle Formulas to find the exact value of each expression. 0 > 0 ɔsɔ 'c- = A uei "61 20. cot 0 = 3, 0 > e soɔ \ 21. sin 22.5° 22. cos 22.5° 23. tan 8 157 24. tan 25. cos 165° 8 26. sin 195° 27. sec 8 29. sin 8 30. cos In Problems 31–42, f(x) = sin x, g (x) = cos x, and h(x) = tan x. Use the figures below to evaluate each function. 31. f(20) 32. g(20) 33. (x, 2) x2 + y2 = 5 x2 + y2 = 1 34. f 35. h(20) y *9E ybb 37. 8(2a) 38. f(2a) n offT (a) 39. 40. g 41. h 42. h(2a) () btained as.t 43. Show that sin* 0 = 3 cos (20) + cos (40). 44. Show that sin ( 40) = (cos 0) (4 sin 0 – 8 sin 0). A 45. Show that sin? 0 cos 0 1. 1. cos ( 40). A 46. Show that sin* 0 cos“ 0 = 128 3. cos (40) + 32 cos ( 80). 48. Find an expression for cos (46) as a fourth-degree polynomial 128 8. in thn expression for cos (30) as a third-degree polynomial the variable cos 0. in the variable cos 0. 50. Find an expression for cos (50) as a fifth-degree polynomial in the variable cos 0. In the variable sin 0. 7.6 Assess Your Understanding 49. Find an expression for sin (50) as a fifth-degree polynomial ాయ parts fa) d 30