C H A P T E R 5 Analytic Trigonometry

480 Chapter 5 Analytic Trigonometry
tan u tan v
47. tanu v
1 tan u tan v
7 3
24 4
1 7
243 4
11 24
39
32
44
117
1
49. secu v
cosu v
Use Exercise 45 for cosu v.
1 3
5
5
3
50.
51.
52. Let
cosu v cos u cos v sin u sin v 24 254 5 7
253 5
96 21 117
125 125 125
48.
tanv u
cotv u
sinarcsin x arccos x sinarcsin x cosarccos x sinarccos x cosarcsin x
x 2 1 x 2
1
θ
1
1 − x 2
θ = arcsin x
u arctan 2x and v arccos x
tan u 2x cos v x.
u
4 x + 1 2
1
sinarctan 2x arccos x sinu v
x x 1 x 2 1 x 2
2x
sin u cos v cos u sin v
2x2 1 x 2
4x 2 1
v
x
2x
4x2 1
x
1 4x2 1 1 x2 1
x
θ
1 − x 2
1
x
θ = arccos x
tan v tan u
1 tan v tan u
11
24
39
32
44
117
34
7
24
1 3 4 7
24
1
tanv u 1 44
117
117
44
1 − x 2