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 =
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 =
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Chapter2: Second-order Linear Odes
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Topic Video
Question
13,19 plz
Transcribed Image 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
Expert Solution
Step 1
Part (13):-
Given that
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