Answers to ch 5 test review
1.
2.
=1
3. sec y (cos y ) = 1,
4.
5.
6.
7. 2cos x sin x – cos x = 0
cos x(2 sin x – 1)
cos x = 0
2sin x – 1 =0
sin x = ½
8.
tan x = 0
9.
0,
10.
11. tan2x = 3
tan x =
12. 2sin2 x = 1
sin x =
13. sin 15 = sin 60 – 45 = sin 60 cos 45 – sin 45 cos 60 =
14. tan 15 = tan 45 – 30 =
15. sin 75 = sin 45 + 30 = sin 45 cos 30 + sin 30 cos 45 =
16. cos 75 = cos 45 + 30 = cos 45 cos 30 – sin 45 sin 30 =
17.
= -.309
18.
19. sin 3x = sinx
sin 3x – sin x = 0 (rewrite sin 3x as sin 2x + x and then use the sin sum identity)
sin 2x + x – sin x = 0
sin 2x cos x + sin x cos 2x – sin x = 0
2sin x cos x cos x + sin x(2cos2 x – 1) – sin x =0 (combine cos x and cos x and distribute)
2sin x cos2x + 2sin x cos2 x – sin x – sin x = 0
4sin x cos2 x – 2 sin x = 0 (combined like terems)
2sin x (2cos2 x – 1) = 0
2 sin x = 0
2cos2x – 1= 0
sin x = 0
cos x = ±
20. sin2x – 2sin x – 3= 0
(sin x + 1)(sin x – 3) = 0
sin x + 1 = 0 sin x – 3 =0
sin x = -1
sin x = 3
ø
21. cos 2t = cos t
cos 2t – cos t =0 (must rewrite cos 2t using the double angle identity)
2cos2 t – 1 – cos t = 0 (rewrite)
2cos2 t – cos t – 1= 0 (factor)
(2cos t + 1)(cos t – 1) =0
2cos t + 1 =0 cos t – 1 = 0
cos t = -1/2
cos t = 1
22. cos 2x + 5 cos x = 2
cos 2x + 5cos x – 2 =0 (rewrite cos 2x using double angle identity)
2cos2 x – 1 + 5cos x – 2 = 0
2cos2 x + 5 cos x – 3 =0
(2cos x – 1)(cos x + 3) = 0
2cos x – 1 =0
cos x + 3 = 0
cos x = ½
cos x = -3
23.
C = 180 – 79 – 33 = 68°
b: (7 sin 33) ÷ sin 79 = 3.9
c: (7 sin 68) ÷ sin 79 = 6.6
24.
Not a triangle because (8sin 30) ÷ 3 = 1.3333 > 1 so the sin is ø
25. A: 52 = 72 + 62 – 2(7)(6)cos A
25 = 85 - 84cos A
-60 = -84cos A
.714… = cos A
cos-1 .714… = 44°
B: 72 = 52 + 62 – 2(5)(6)cos B
49 = 61 – 60 cos B
-12 = -60 cos B
.2 = cos B
cos-1 .2 = 78°
C: 180 – 44 – 78 = 58°
2
26. c: 62 = 44 + c2 – 2(4)(c)cos 85
36 = 16 + c2 – .697245942c (bring everything to one side and do quadratic formula)
c2 - .697245942c – 20 = 0
=
4.83 and -4.14
= 4.83
B: 42 = 63 + 4.832 – 2(6)(4.83)cos B
16 = 59.3289 – 57.96 cos B
-43.3289 = - 57.96 cos B
.7475… = cos B
cos-1 .7475… = 42°
C: 180 – 85 – 52 = 53°
27. use Heron’s formula:
s = ½(3 + 5 + 6) = 7
28. use area formula with sines:
½(10)(6)sin 50
= 22.98
29. DRAW a picture first
a.
b. 102. 5 ft (finding a)
(finding x)
30. DRAW a picture first
x2 = 2502 + 9502 – 2(250)(950)cos 70
x2 = 802540.4319
x = 895.85 ft
31. (3/4)2 + 1 = sec2 x
(9/16) + 1 = sec2x
25/16 = sec2x
sec x = 5/4
so cos x = 4/5 and sin x = 3/5
5
3
4
32. tan2 x + 1 = (4)2
tan2 x + 1 = 16
tan2 x = 15
tan x = cot x = 33.
34.
35. cos 18 + 39 = cos 57°
36. sin
1
4
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