C H A P T E R 5 Analytic Trigonometry

456 Chapter 5 Analytic Trigonometry
49.
51.
53.
54.
55.
56. (a)
sin 2 x sin 4 x cos x sin 2 x1 sin 2 x cos x 50.
sin 2 x cos 2 x cos x
sin 2 x cos 3 x
sin 2 25 sin 2 65 sin 2 25 cos 2 90 65 52.
sin 2 25 cos 2 25
1
cos 2 20 cos 2 52 cos 2 38 cos 2 70 cos 2 20 cos 2 52 sin 2 90 38 sin 2 90 70
cos 2 20 cos 2 52 sin 2 52 sin 2 20
cos 2 20 sin 2 20 cos 2 52 sin 2 52
1 1
sin 2 12 sin 2 40 sin 2 50 sin 2 78 sin 2 12 sin 2 78 sin 2 40 sin 2 50
cos x csc x cot x cos x 1
sin x
(b)
h sin90
sin
10
1
cos x1
sin2 x
cos x1 csc 2 x
cos xcsc 2 x 1
cos x cot 2 x
20
cos x
sin x
h cos
h cot
sin
30
40
2
cos 2 90 12 sin 2 78 cos 2 90 40 sin 2 50
cos 2 78 sin 2 78 cos 2 50 sin 2 50
1 1 2
s 28.36 13.74 8.66 5.96 4.20 2.89 1.82 0.88 0
50
57. False. For the equation to be an identity,
it must be true for all values of in the domain.
60
70
80
sin 4 x cos 4 x sin 2 x sin 2 x cos 4 x
1 cos 2 x1 cos 2 x cos 4 x
1 2 cos 2 x cos 4 x cos 4 x
1 2 cos 2 x 2 cos 4 x
cos 2 55 cos 2 35 cos 2 55 sin 2 90 35
90
cos 2 55 sin 2 55
1
58. True. An identity is an equation that is true for all
real values in the domain of the variable.
59. Since then
if lies in Quadrant III or IV. One
such angle is 7
4 .
sin 1 cos2 sin ±1 cos
2 sin ;
2 1 cos2 , 60.
True identity:
tan sec is not true for 2 < <
32 < < 2. Thus, the equation is not true for
or
2 tan ±sec
1
2 tan sec
1
2 1
34.
(c) Greatest: 10,
Least: 90
(d) Noon