C H A P T E R 5 Analytic Trigonometry

444 Chapter 5 Analytic Trigonometry
66.
5 tan x sec x 5tan x sec x
tan x sec x tan x sec x tan2 x sec2 x
5tan x sec x
1
5sec x tan x
67.
3 sec x tan x 3sec x tan x
sec x tan x sec x tan x sec2 x tan2 x
3sec x tan x
1
3sec x tan x
68. tan4 tan xcsc x 1
2 xcsc x 1 tan2 x
tan2 xcsc x 1
cot2 tan
x
2 x csc x 1
csc x 1 csc x 1 tan2 xcsc x 1
csc2 x 1
69.
y1 cos
2 x , y2 sin x
x 0.2 0.4 0.6 0.8 1.0 1.2 1.4
y 1
y 2
0.1987 0.3894 0.5646 0.7174 0.8415 0.9320 0.9854
0.1987 0.3894 0.5646 0.7174 0.8415 0.9320 0.9854
70. y 1 sec x cos x, y 2 sin x tan x
71.
x 0.2 0.4 0.6 0.8 1.0 1.2 1.4
y 1
y 2
y 1
0.0403 0.1646 0.3863 0.7386 1.3105 2.3973 5.7135
0.0403 0.1646 0.3863 0.7386 1.3105 2.3973 5.7135
x 0.2 0.4 0.6 0.8 1.0 1.2 1.4
y 1
y 2
cos x
1 sin x , y 1 sin x
2
cos x
1.2230 1.5085 1.8958 2.4650 3.4082 5.3319 11.6814
1.2230 1.5085 1.8958 2.4650 3.4082 5.3319 11.6814
72. y 1 sec 4 x sec 2 x, y 2 tan 2 x tan 4 x
x 0.2 0.4 0.6 0.8 1.0 1.2 1.4
y 1
y 2
0.0428 0.2107 0.6871 2.1841 8.3087 50.3869 1163.6143
0.0428 0.2107 0.6871 2.1841 8.3087 50.3869 1163.6143
73. y1 cos x cot x sin x csc x
cos x
cos x cot x sin x cos x sin x
sin x
cos2 x
sin x sin2 x
sin x
cos2 x sin 2 x
sin x
1
csc x
sin x
1200
0
0
1
0
0
Conclusion: y 1 y 2
6
0
0
2
2
It appears that y 1 y 2 .
12
0
1
Conclusion: y 1 y 2
2
It appears that y 1 y 2 .
−2 2
4
−4
2