C H A P T E R 5 Analytic Trigonometry

40.
42.
44.
sin x
2 3
2
x
2
4
2n
3
x 8
4n
3
sin x cos x 0
or
x
2
y sin x cos x
sin x cos x
x
n
4
x 1
n
4
5
2n
3
x 10
4n
3
For the intercepts are 1 3 7 11
, , ,
4 4 4 4 .
1 < x < 3
sec 4
x
sec 4
x
sec 8 ±2
x
x 8
y sec 4
8 4 0
8 4
x
4 2 n
x 2 4n
For 3 < x < 3 the intercepts are 2 and 2.
Section 5.3 Solving Trigonometric Equations 463
41.
43.
y sin
From the graph in the textbook we see that the
curve has x-intercepts at x 1 and at x 3.
x
1
2
In general, we have:
sin x
2 1
x
2
3
2n
2
x 3 4n
y tan
From the graph in the textbook we see that
the curve has x-intercepts at x ±2.
2 x
6 3
In general, we have:
tan2 x
6 3
8 4 45. Graph y1 2 sin x cos x.
46. 4 sin3 x 2 sin2 x 2 sin x 1 0 47. Graph y1
0
4
−2
2
x 0.785, 2.356, 3.665, 3.927, 5.498, 5.760
0
4
−4
The x-intercepts occur at
x 2.678 and x 5.820.
0
10
−10
tan x
6 ±3
2
1 sin x
cos x
x
6
± n
3
x ±2 6n
The x-intercepts occur at
and x 5
x 1.047
5.236.
3 3
2
cos x
4.
1 sin x