The Inverse Sine, Cosine, And Tangent Functions Worksheet Template Page 5
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6Example: Find the exact value of the composite function. Notice that the inverse function is on the inside.
2
1
cos cos
a)
When the inverse cosine function is on the inside, the x-value must be between -1 and 1.
3
2
2
Since
is in this interval, the answer is simply
.
3
3
1
tan tan
2
x
b)
When inverse tangent is on the inside, the x-value can be any real number
.
1
tan tan
2
Therefore, since -2 is a real number, then
= ______________.
1
sin sin
2
c)
When inverse sine is on the inside, the x-value must be between -1 and 1. Since -2 is NOT in
this interval, we say the answer is "Not Defined".
1
cos cos
1.5
d)
When inverse cosine is on the inside, the x-value must be between -1 and 1. Since 1.5 is NOT
in this interval, the answer is _______________________________________.
FINDING THE INVERSE FUNCTION OF A TRIGONOMETRIC FUNCTION
f x
( )
We do this using the same steps we did in college algebra and precalculus. Step 1) Replace
with y. Step 2) Switch all
1
f
( )
x
y's and x's. Step 3) Solve for y. Step 4) Replace y with
.
-1
Example: Find the inverse function and state the domain and range of f and f
.
f x
( ) 2tan
x
3
a)
f x
( ) cos
x
2
1
b)
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