Section 7.1 The Inverse Sine, Cosine, and Tangent Functionsfaculty.montgomerycollege.edu/maronne/Ma180/power...1 ( ) 1. Find the inverse function of 3cos 1, . 22 Find the range of

Section 7.1

The Inverse Sine, Cosine, and Tangent Functions

Copyright © 2013 Pearson Education, Inc. All rights reserved

Review of Properties of Functions and Their Inverses











5 is not in the interval , so 8 2 2

we need an angle in the interval 5, for which sin sin .

2 2 8

π π π

π π πθ

−

− =








1 5(a) cos cos6π−

( )1(b) cos cos 0.2−

1 5(c) cos cos4π−

( )1(d) cos cos 2−

[ )5 5 = since is in the interval 0, .6 6π π π

[ ] = 0.2 since 0.2 is in the interval 1,1 .−

[ )5 Since is not in the interval 0, we find an angle that has the same 4

5 3cosine value that is in that interval. cos cos4 4

π π

π π =

1 3 3 = cos cos4 4π π− =

[ ]This is undefined since 2 is not the interval 1,1 .−




−2 −1 1 2

−π/2

−π/4

π/4

π/2

1tan−=y xCopyright © 2013 Pearson Education, Inc. All rights reserved

−3 −2 −1

−π/2

−π/3

−π/6

π/6

π/3

1tan−=y x




( )1

1

Find the inverse function of 3cos 1, .2 2

Find the range of and the domain and range of .

f f x x x

f f

π π−

−

= + − ≤ ≤

3cos 1y x= +

3cos 1x y= + interchange x and y

3cos 1y x= −

1cos3

xy −=

( )1 11cos3

xy f x− −− = =

Recall that the domain of f is the range of f-1 and the range of f is the domain of f-1.

1 1Domain of is 1 13

xf − −− ≤ ≤

3 1 3x− ≤ − ≤ 2 4x− ≤ ≤

1

So the range of is 2 4

and the range of is , .2 2

f y

f π π−

− ≤ ≤

−



1Solve the equati 2coson: 2

x π− =

1os4

c x π− =

s4

cox π=

22

x =


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Section 7.1 The Inverse Sine, Cosine, and Tangent Functionsfaculty.montgomerycollege.edu/maronne/Ma180/power...1 ( ) 1. Find the inverse function of 3cos 1, . 22 Find the range of