25,31 plz ION 7.6 Double-angle and Half-angle Formulas 5077.6 Assess Your Understanding2V5Concepts and Vocabulary7. Multiple Choice Choose the expression that completes theHalf-angle Formula for cosine functions: cos1. cos (20) = cos 01-cos 0cos a1+ cos a2. sin(a) t(b) +2(d)1 cos 0cos asin a1- cos a3. tan5(c) +(d) +V1 + cos acontain + and-2 tan 04. True or False tan (20) =1tan ecos 0then which8. Multiple Choice If sin a = ±.s True or False sin (20) has two equivalent forms:2 sin e cos 0 and sin? 0 - cos? A( True or False tan (20) + tan (20) = tan(40)ormulasstatement describes how e is related to a?(a) 0 = a(b) 0 =(c) 0 = 2a (d) 0 = a?Formula (9)Skill BuildingProblems 9-20, use the information given about the angle 0, 0se < 27, to find the exact value of:(a) sin (20)(b) cos (20)(c) sin(d) cosDouble-angle Form3310. cos 0 =5'411. tan 0 =TT0 < 0 <5'>0 > 0< 0 019. tan 0 = -3, sin e < 020. cot 0 = 3, cos 0 < 018. sec 0 = 2, csc 0 < 0tanIn Problems 21-30, use Half-angle Formulas to find the exact value of each expression.\21. sin 22.5°22. cos 22.5°23. tan824. tan815727. sec8728. csc826. sin 195°25. cos 165°3730. cos29. sinIn Problems 31-42, f(x) = sin x, g(x) = cos x, and h(x) = tan x. Use the figures below to evaluate each function.y31. f(20)32. g(20)x2 + y2 = 5x2 + y2 = 1(х, 2)3A.33. gl35. h(20)36.nogab0 ne lo a o38. f(2u) a T ()37. g(2a)42. h(2a)41. h39.40.A slumoltained as i44. Show that sin (40) = (cos 0) (4 sin 0 – 8 sin° 0).343. Show that sin“ 0 =81cos (20) + cos (46).1cos (80).3A 46. Show that sin" 0 cos“ e =1281cos (40) + 128°1132A 45. Show that sin? 0 cos² 0cos (40).48. Find an expression for cos ( 40) as a fourth-degree polynomialin the variable cos 0.84%. Find an expression for cos ( 30) as a third-degree polynomialin the variable cos 0.49. Find an expression for sin ( 50) as a fifth-degree polynomialin the variable sin 0.50. Find an expression for cos ( 50) as a fifth-degree polynomialin the variable cos 0.the results of

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Description: 25,31 plz ION 7.6 Double-angle and Half-angle Formulas 5077.6 Assess Your Understanding2V5Concepts and Vocabulary7. Multiple Choice Choose the expression that completes theHalf-angle Formula for cosine functions: cos1. cos (20) = cos 01-cos 0cos a1+

Note- as we are allowed to answer one question in one session so, i ahve answered question 25 for…

Answered: 25. cos 165°

Math

Calculus

25. cos 165°

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.4: Multiple-angle Formulas

Problem 67E

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Topic Video

Question

25,31 plz

ION 7.6 Double-angle and Half-angle Formulas 507
7.6 Assess Your Understanding
2V5
Concepts and Vocabulary
7. Multiple Choice Choose the expression that completes the
Half-angle Formula for cosine functions: cos
1. cos (20) = cos 0
1-cos 0
cos a
1+ cos a
2. sin
(a) t
(b) +
2
(d)
1 cos 0
cos a
sin a
1- cos a
3. tan5
(c) +
(d) +
V1 + cos a
contain + and-
2 tan 0
4. True or False tan (20) =
1
tan e
cos 0
then which
8. Multiple Choice If sin a = ±.
s True or False sin (20) has two equivalent forms:
2 sin e cos 0 and sin? 0 - cos? A
( True or False tan (20) + tan (20) = tan(40)
ormulas
statement describes how e is related to a?
(a) 0 = a
(b) 0 =
(c) 0 = 2a (d) 0 = a?
Formula (9)
Skill Building
Problems 9-20, use the information given about the angle 0, 0se < 27, to find the exact value of:
(a) sin (20)
(b) cos (20)
(c) sin
(d) cos
Double-angle Form
3
3
10. cos 0 =
5'
4
11. tan 0 =
TT
0 < 0 <
5'
>0 > 0
< 0 <T
3' T <0 <
V3 37
3' 2
9. sin 0 =
2
37
12. tan 0 =
2'
1
T <0 <
13. cos e = -
e < 27
14. sin 0 =
3' 2
in
16. csc e =
- V5, cos e < 0
17. cot 0 = -2, sec 0 < 0
15. sec 0 = 3, sin 0 > 0
19. tan 0 = -3, sin e < 0
20. cot 0 = 3, cos 0 < 0
18. sec 0 = 2, csc 0 < 0
tan
In Problems 21-30, use Half-angle Formulas to find the exact value of each expression.
\21. sin 22.5°
22. cos 22.5°
23. tan
8
24. tan
8
157
27. sec
8
7
28. csc
8
26. sin 195°
25. cos 165°
37
30. cos
29. sin
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.
y
31. f(20)
32. g(20)
x2 + y2 = 5
x2 + y2 = 1
(х, 2)
3A.
33. gl
35. h(20)
36.
nogab0 ne lo a o
38. f(2u) a T ()
37. g(2a)
42. h(2a)
41. h
39.
40.
A slumol
tained as i
44. Show that sin (40) = (cos 0) (4 sin 0 – 8 sin° 0).
3
43. Show that sin“ 0 =
8
1
cos (20) + cos (46).
1
cos (80).
3
A 46. Show that sin" 0 cos“ e =
128
1
cos (40) + 128°
1
1
32
A 45. Show that sin? 0 cos² 0
cos (40).
48. Find an expression for cos ( 40) as a fourth-degree polynomial
in the variable cos 0.
8
4%. Find an expression for cos ( 30) as a third-degree polynomial
in the variable cos 0.
49. Find an expression for sin ( 50) as a fifth-degree polynomial
in the variable sin 0.
50. Find an expression for cos ( 50) as a fifth-degree polynomial
in the variable cos 0.
the results of

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