C H A P T E R 5 Analytic Trigonometry

56.
3 tan 2 x 4 tan x 4 0
tan x 4 ± 42 434
23
tan x 2 tan x 2
3
x arctan2 n x arctan 2
n 3
1.1071 n 0.5880 n
The values of x in 0, 2 are 0.5880, 3.7296, 2.0344, 5.1760.
4 ± 64
6
Section 5.3 Solving Trigonometric Equations 465
2, 2
3
57. tan2 x 3 tan x 1 0 Graph y1 tan2 x 3 tan x 1.
58.
tan x
3 5
2
tan x 3 ± 32 411
21
or tan x
3 5
2
x 1.9357, 5.0773 x 2.7767, 5.9183
3 ± 5
2
4 cos 2 x 4 cos x 1 0 59.
cos x
No solution
Solutions in are and
1 2
1.7794, 4.5038.
2 :
1 2
0, 2 arccos 2
7
0 2
−3
1 2
2
1 2
x arccos 2
1.7794
2 arccos
cos x 4 ± 42 441
24
4 ± 32
8
cos x
1 ± 2
2
1 2
2
1 2
> 1 2
0
10
−5
0
50
−10
2
The x-intercepts occur at x 1.9357, x 2.7767,
x 5.0773, and x 5.9183.
tan 2 x 6 tan x 5 0
tan x 1tan x 5 0
tan x 1 0 or tan x 5 0
tan x 1 tan x 5
x 5
,
4 4
2
x arctan 5, arctan 5