13,19 plz SECTION 7.6 Double-angle and Half-angle Formulas 507concepts and Vocabulary0soɔ = (07) s03e soɔ - I27. Multiple Choice Choose the expression that completes theHalf-angle Formula for cosine functions: cos-2. sin%3D2.1+ cos a) so) - I2.cos a- sin ae soɔ - I+ (B)3. tan 2I (9)2 tan 0cos a4. True or False tan (20)I (3)tan? 0+ (P)s True or False sin ( 20) has two equivalent forms:D soɔ + I8. Multiple Choice If sin a = ±2 sin 0 cos 0statement describes how 0 is related to a?then which6. True or False tan ( 20) + tan (20) = tan (40)0 „soɔ - 0 „UỊS punProblems 9-20, use the information given about the angle 0,0 s 0 < 27, to find the exact value of:సబ0 = e (B)30 (q)Skill Building0 = 0 (p) 07 = 0 ()(a) sin (20)(b) cos (20)Cuis (2)soɔ (p)= e uis 65 *3.= e soɔ "0I5.,>0 >011. tan 0 =3°212. tan 0 =2°> e > 09A3' 213. cos 0 = --> 0 > 4> 0 > uV3 3714. sin 0 =15. sec 0 = 3,L > 0>-sin 0 > 0216. csc 0 = -V5, cos 0 < 0<0 < 2718. sec 0 = 2,17. cot 0 -2,0 > 0 ɔəs0 > e uISIn Problems 21-30, use Half-angle Formulas to find the exact value of each expression.0 > 0 ɔsɔ'c- = A uei "6120. cot 0 = 3,0 > e soɔ\ 21. sin 22.5°22. cos 22.5°23. tan815724. tan25. cos 165°826. sin 195°27. sec829. sin830. 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)32. g(20)33.(x, 2)x2 + y2 = 5x2 + y2 = 134. f35. h(20)y *9Eybb37. 8(2a)38. f(2a) n offT (a)39.40. g41. h42. h(2a)()btained as.t43. Show that sin* 0 =3cos (20) +cos (40).44. Show that sin ( 40) = (cos 0) (4 sin 0 – 8 sin 0).A 45. Show that sin? 0 cos 01.1.cos ( 40).A 46. Show that sin* 0 cos“ 0 =1283.cos (40) +32cos ( 80).48. Find an expression for cos (46) as a fourth-degree polynomial1288.in thn expression for cos (30) as a third-degree polynomialthe 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 0.7.6 Assess Your Understanding49. Find an expression for sin (50) as a fifth-degree polynomialాయparts fa) d30

Name: 13,19 plz SECTION 7.6 Double-angle and Half-angle Formulas 507concepts
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Description: 13,19 plz SECTION 7.6 Double-angle and Half-angle Formulas 507concepts and Vocabulary0soɔ = (07) s03e soɔ - I27. Multiple Choice Choose the expression that completes theHalf-angle Formula for cosine functions: cos-2. sin%3D2.1+ cos a) so) - I2.cos a-

Part (13):- Given that cosθ = - 63, π2<θ<π

Answered: 0 > 0 soɔ 19. ta 0 = -3, sin 0 <0 = 0…

Math

Advanced Math

0 > 0 soɔ 19. ta 0 = -3, sin 0 <0 = 0 ɔsɔ "9I 16. csc e = - V5, cos 6 <0 3. L > 0> 2 3 13. cos 0 =

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Topic Video

Question

13,19 plz

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

Expert Solution

Step 1

Part (13):-

Given that $\cos θ = - \frac{\sqrt{6}}{3}, \frac{π}{2} < θ < π$

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