C H A P T E R 5 Analytic Trigonometry

502 Chapter 5 Analytic Trigonometry
61.
2 cos x 1 0, 5or cos x 1 0
x 5
, ,
3 3
3, , and 53 are all solutions to the equation.
0
2
−2
63. 6 sin
4
cos
1 cos x
± sin x
2
x
sin x 0 62.
2
1 cos x
sin
2
2 x
1 cos x 2 sin 2 x
1 cos x 2 2 cos 2 x
2 cos 2 x cos x 1 0
2 cos x 1cos x 1) 0
cos x 1
, 5or 1cos x 1
2
x 5
, or cos 1x
3 3
2
1
cos 6
4 2
sin 4
4
sin
4 4
cos xcos x 1 0
cos x 0 or cos x 1 0
0, and are all solutions to the equation.
2
2 ,
0
3
−3
3sin sin 0 2
tan x
gx tan
sin x 0
2 x
sin x
2
1 cos x
sin x
sin x
1 cos x sin 2 x
1 cos x 1 cos 2 x
cos 2 x cos x 0
x 3
,
2 2
7
7
64. 4 cos 2sin 2sin 6 sin 5 1 5 5
sin 4 sin
3 6 3 6 sin
3 6
2
65. 10 cos 75 cos 15 10 1
2cos75 15 cos75 15 5cos 60 cos 90
66. 6 sin 45 cos 15 6 3sin 60 sin 30
1
2 sin 60 sin 30
67. 1
cos 4 sin 6 2sin 10 sin 2
1
2sin 10 sin2
2sin4 6 sin4 6 1
3
2
2
cos x 1
68. 3
2 cos cos 5
3
3 sin 2 sin 3 3 2 cos cos 5
1
69.
5 cos5 cos 3 5 1
2cos2 3 cos2 3
2cos5 3 cos5 3 5
5
2cos 8 cos 2
2 cos8 cos2
70. 1
2cos 2 cos 6
1
cos 2 cos 4 2cos2 cos 6
1
2cos2 4 cos2 4
6
x 0
sin 2
71. sinx y sinx y 1
2cos 2y cos 2x 72. sinx y cosx y 1
2sin 2x sin 2y