37 plz 47. Find an expression for cos (30) as a third-degree polynomial49. Find an expression for sin (50) as a fifth-degree polynomial7.67. Multiple Choice Choose the expression that completes theHalf-angle Formula for cosine functions: cos =1. cos (20) = cos o-1- cos 0%3D2 sin2- cos a1 + cos a(a) +(b) ±1- cos 0%3D1 tan5(c) +cos asin a1- cos a2 tan 02(d)V1 + cos a4 True or False tan (20) =1 - tan? 08. Multiple Choice If sin a = ±.cos 6, then which2statement describes how 0 is related to a?2 sin e cos e and sin? 0 – cos² ATrựe or False tan (20) + tan(20) = tan(40)(a) 0 = a(b) 0 =(c) 0 = 2a (d) 0 = a²Skill BuildingTablems 9-20, use the information given about the angle 0,0 s 0 < 27, to find the exact value of:(b) cos (20)(c) sin (d) cos(a) sin (20)2sin 0 =5'10. cos 0 =0 < 0 <55'11. tan 0 =33mV6V3 3712. tan 0 =2°T < 0 < =13. cos e =TT- < 0 < T< 0 < 2m214. sin 0 =15. sec 0 = 3, sin 0 > 016. csc e = -V5, cos 0 < 017. cot 0 = -2, sec 0 <018. sec 0 = 2, csc 0 < 019. tan 0 = -3, sin 0 < 020. cot 0 = 3, cos e < 0In Problems 21–30, use Half-angle Formulas to find the exact value of each expression.\ 21. sin 22.5°924. tan822. cos 22.5°23. tan8thet the pro d15727. sec825. cos 165°26. sin 195°28. csc829. sir30. cosIn 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)yy32. g(20)x2 + y2 = 5x2 + y2 = 1(х, 2)()33.34. f35. h(20)36. hnos0 e le38. f(2a)31. g(2a)39.41. h42. h(2a)40. g343. Show that sine =44. Show that sin (40)= (cos 0) (4 sin 0 - 8 sin 0).1cos (20) +cos (40).88.3145. Show that sin? 0 cos² 0 =A 46. Show that sin 0 cos e =128cos (40) +321cos (80).112888 cos (40).48. Find an expression for cos ( 40) as a fourth-degree polynomialin the variable cos 0.in the variable cos 0.50. Find an expression for cos (50) as a fifth-degree polynomialin the variable cos 0.in the variable sin 0.

Name: 37 plz 47. Find an expression for cos (30) as a third-degree polynomia
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Description: 37 plz 47. Find an expression for cos (30) as a third-degree polynomial49. Find an expression for sin (50) as a fifth-degree polynomial7.67. Multiple Choice Choose the expression that completes theHalf-angle Formula for cosine functions: cos =1. cos

Given: The function gx=cosx and angle α as in figure To determine: The value of g2α.

Answered: 31. g(2a)

Math

Trigonometry

31. g(2a)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.3: Trigonometric Functions Of Real Numbers

Problem 67E

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Question

37 plz

47. Find an expression for cos (30) as a third-degree polynomial
49. Find an expression for sin (50) as a fifth-degree polynomial
7.6
7. Multiple Choice Choose the expression that completes the
Half-angle Formula for cosine functions: cos =
1. cos (20) = cos o-
1- cos 0
%3D
2 sin
2
- cos a
1 + cos a
(a) +
(b) ±
1- cos 0
%3D
1 tan5
(c) +
cos a
sin a
1- cos a
2 tan 0
2
(d)
V1 + cos a
4 True or False tan (20) =
1 - tan? 0
8. Multiple Choice If sin a = ±.
cos 6
, then which
2
statement describes how 0 is related to a?
2 sin e cos e and sin? 0 – cos² A
Trựe or False tan (20) + tan(20) = tan(40)
(a) 0 = a
(b) 0 =
(c) 0 = 2a (d) 0 = a²
Skill Building
Tablems 9-20, use the information given about the angle 0,0 s 0 < 27, to find the exact value of:
(b) cos (20)
(c) sin (d) cos
(a) sin (20)
2
sin 0 =
5'
10. cos 0 =
0 < 0 <5
5'
11. tan 0 =
3
3m
V6
V3 37
12. tan 0 =
2°
T < 0 < =
13. cos e =
TT
- < 0 < T
< 0 < 2m
2
14. sin 0 =
15. sec 0 = 3, sin 0 > 0
16. csc e = -V5, cos 0 < 0
17. cot 0 = -2, sec 0 <0
18. sec 0 = 2, csc 0 < 0
19. tan 0 = -3, sin 0 < 0
20. cot 0 = 3, cos e < 0
In Problems 21–30, use Half-angle Formulas to find the exact value of each expression.
\ 21. sin 22.5°
9
24. tan
8
22. cos 22.5°
23. tan
8
thet the pro d
157
27. sec
8
25. cos 165°
26. sin 195°
28. csc
8
29. sir
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)
y
y
32. g(20)
x2 + y2 = 5
x2 + y2 = 1
(х, 2)
()
33.
34. f
35. h(20)
36. h
nos0 e le
38. f(2a)
31. g(2a)
39.
41. h
42. h(2a)
40. g
3
43. Show that sine =
44. Show that sin (40)
= (cos 0) (4 sin 0 - 8 sin 0).
1
cos (20) +
cos (40).
8
8.
3
1
45. Show that sin? 0 cos² 0 =
A 46. Show that sin 0 cos e =
128
cos (40) +
32
1
cos (80).
1
128
8
8 cos (40).
48. Find an expression for cos ( 40) as a fourth-degree polynomial
in 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.

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