Download Sec 1.7 Inverse Trig Functions

Section 1.7
Inverse Trigonometric
Functions
Essential Question:
•How
do we define the inverse of
the sine, cosine, and tangent
functions?
1
The notation sin x is consistent with the
1
inverse notation f ( x) . The arcsin x
notation comes from the association of a
central angle with its intercepted arc
length on a unit circle. So arcsin x
means the angle (or arc) whose sin is x.
Example 1. Find the exact value of the
expression if it is defined:
1
a ) sin  
2
 3
c) arcsin 

 2 
 1
b) sin   
 2
d ) arcsin 2
1
1
Inverse Cosine Function
The inverse cosine function is the function
cos–1 with domain [–1, 1] and range [0, π],
defined by:
cos–1 x = y

cos y = x
Ex 2. Find the exact value of the
expression if it is defined
 3
a ) cos  
 2 
 
1
b) cos1 0

2
c) arccos  

 2 
Ex 3. Find the exact value of the
expression if it is defined:
 3
a ) cos 

 2 
1
d ) sin 1 1
e) arctan
b) arcsin 0

2
c) arccos  

2


 3
 3
f ) tan 

3


1
Ex 4. Find the exact value of the expression, if it
is defined.
a.)
b.)
 
arcsin  sin 
4

1
tan(tan 1)

  
c.) cos  cos    
 3 

1
Ex 5. Find the exact value of the expression, if it
is defined.
2 

a.) sin  cos 
3 

1
1

b.) tan  arcsin 
2

5 

c.) sin  cos 
6 

1
HW#8 Inverse
Worksheet