C H A P T E R 5 Analytic Trigonometry

466 Chapter 5 Analytic Trigonometry
60.
61.
63. (a) fx sin x cos x
(b)
sec 2 x tan x 3 0
1 tan 2 x tan x 3 0
tan 2 x tan x 2 0
tan x 2tan x 1 0
tan x 2 0
tan x 2
Maximum:
Minimum:
cos x sin x 0
f
4
f 5
4
x arctan2 n
1.1071 n
Solutions in are arctan2 2, 5
,
4 4 .
0, 2 arctan2 ,
cos x sin x
1
tan x 1
sin
4
, 2 4
5
, 2 4
sin 5
4
sin x
cos x
x 5
,
4 4
tan x 1 0
tan x 1
2 2
cos 2
4 2 2
x arctan1 n
n
4
2 cos 2 x 5 cos x 2 0 62.
2 cos x 1cos x 2 0
2 cos x 1 0 or cos x 2 0
cos x 1
2
x 5
,
3 3
cos x 2
No solution
0 2
5
cos sin
4 4
cos 4 2
2
2 2 2
3
−3
2 sin 2 x 7 sin x 3 0
sin x 32 sin x 1 0
sin x 3 0
No solution
2 sin x 1 0
Solutions in 0, 2 are 5
,
6 6 .
sin x 1
2
x 5
,
6 6
Therefore, the maximum point in the interval 0, 2 is 4, 2 and the minimum point is 54, 2 .