Download 7.1 Inverse Sine Cosine Tangent Functions

Precalculus 7.1 The Inverse Sine, Cosine, & Tangent Functions
Objective: able to find the exact value of an inverse sine, cosine, or tangent function; find and approx. value of an inverse
sine function; use properties of inverse functions to find exact values of certain composite functions; find the inverse
function of a trigonometric function; solve equations involving inverse trig. functions
Recall from Section 5.2 regarding inverse functions:
−1
1. For every x in the domain of f, f ( f ( x )) = _____
2. For every
x in the domain of f -1,
3. Domain of
4. Range of
.
f ( f −1 ( x )) = _____ .
f = Range of ____
f = Domain of ____
5. The graph of
f and the graph of f -1 are symmetric with respect to ________
y = f(x) has an inverse function, then the implicit inverse function is __________, and
solving for y, we get___________.
6. If a function
Graph the inverse sine function and state its domain and range.
For what values of
x is sin −1 (sin x ) = x
?
For what values of
x is sin(sin −1 x ) = x
?
1. Find the exact value of sin-1 1.
3. Find the exact value of sin-1
2. Find the exact value of sin-1 0.

3
−

 2 


5. Use a calculator to evaluate sin
-1
4. Find the exact value of
0.6 to the nearest hundredths.
Graph the inverse cosine function and state its domain and range.
 5π 
sin −1  sin

6 

For what values of
x is cos −1 (cos x ) = x
?
For what values of
x is cos(cos −1 x ) = x
?
6. Find the exact value of cos-1 1.
-1
8. Find the exact value of cos
7. Find the exact value of cos-1 0.

3
−

 2 


10. Use a calculator to evaluate cos
-1
9. Find the exact value of
0.6 to the nearest hundredths.
Graph the inverse tangent function and state its domain and range.
  7π
cos −1 cos
  5

 .

For what values of
x is tan −1 (tan x) = x
?
For what values of
x is tan(tan −1 x ) = x
?
11. Find the exact value of tan-1 1.
13. Find the exact value of
( )
tan −1 3
12. Find the exact value of tan-1 0.
.
14. Find the exact value of
 
3 

tan −1  tan  −

  2 
15. Use a calculator to evaluate tan-1 0.6 to the nearest hundredths.
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