C H A P T E R 5 Analytic Trigonometry

460 Chapter 5 Analytic Trigonometry
15.
17.
19.
21.
23.
4 cos 2 x 1 0 16.
cos 2 x 1
4
cos 2 x ± 1
2
x n
3
cos 3 x cos x 0
cos xcos 2 x 1 0
or x 2
n
3
2 sin 2 2x 1 18.
sin 2x ± 1
±2
2 2
2x
4
2x 5
4
Thus,
We can combine these as follows:
x
8
3
2n, 2x 2n,
4
x
8
7
2n, 2x 2n
4
n, 3
8
n
2
n, 5
8
3 n
, x
8 2
cos 3 x cos x 22.
cos x 0, 3 or cos 2 x 1 0
x 3
,
2 2 or 2 1cos x ±1
cos x 0, 3 or cos 2 1x 0,
7
n, n.
8
tan 3xtan x 1 0 20.
tan 3x 0 or tan x 1 0
3x n tan x 1
x n
3
3 tan 3 x tan x 0
tan x3 tan 2 x 1 0
x n
4
tan x 0, or 3 tan 2 x 1 0
tan x 0, or 3 2 1tan x ± 3
3
tan x 0, or 32 1tan x 5 7 11
, , ,
6 6 6 6
sin 2 x 31 sin 2 x 0
tan 2 3x 3
tan 3x ±3
or
3x
3
3x 2
3
cos 2x 0
2x
n
2
x n
4 2
sec 2 x 1 0
sec 2 x 1
sec x ±1
sin 2 x 3 cos 2 x
4 sin 2 x 3
sin x ± 3
2
cos 2x2 cos x 1 0
x 0 or x
x n
3
n
n ⇒ x
9 3
2 n
n ⇒ x
9 3
or
or x 2
3
2 cos x 1 0
cos x 1
2
n
x 2
2n
3
or x 4
2n
3