Name_____________________________________
Graphing Inverse Trig Functions
Date______
10H Per___
Warm-Up: Given relation A = {(1, 3), (8, 5), (7, 3)}
a) Is it a function?
b) What is the domain?
d) Is the inverse of A a function? Why or why not?
e) What is the inverse of A?
The notations for the inverse trig functions are as follows:

arcsin(x) = sin-1(x)
o "the angle whose sine is x"

Working with inverse trig functions:
Find the exact value of each
1
2
Ex. 1: arcsin  
arccos(x) = cos-1(x)
o i.e. arccos(1/2): the angle whose cosine is 1/2
o cosθ = 1/2

c) What is the range?



Ex. 2: tan 1  
3

3 
arctan(x) = tan-1(x)
o tan-1(1) =

 1 
 
Ex. 3: sin  arccos   
2

Graphing y = arcsin(x) or y = sin-1(x)
- We must restrict the domain of f ( x)  sin( x) to ___________________so that the inverse, f (x)  sin1(x) , is a
function.
- To graph the inverse of a function, switch the _____ and _____ values.
y

x


sinx
x
sin-1(x)
2
0

2
x
For y = sin-1(x), identify:
Domain:
*Memory Trick*
Range:
Graphing y = arccos(x) or y = cos-1(x)
- We must restrict the domain of f ( x)  cos( x) to ___________________so that the inverse, f ( x)  cos1 ( x) , is a
function.
x
cosx
y
cos-1(x)
x
0

2

x
For y = cos-1(x), identify:
Domain:
*Memory Trick*
Range:
Graphing y = arctan(x) or y = tan-1(x)
- We must restrict the domain of f ( x)  tan( x) to ___________________so that the inverse, f ( x)  tan 1 ( x) , is a
function.
y
x


tanx
x
tan-1(x)
4
0

4
x
For y = tan-1(x), identify:
Domain:
*Memory Trick*
Range:

 2 
 
Ex. 4: Find the exact value of tan sin 1   
3


 4 
 
Ex. 5: Find the exact value of sin  arccos   
7

Homework:
1. Find the exact value of each:
 3 

 3 
a) tan1

 2 

 2 

c) cosarcsin1
b) arcsin
 6 


d) sin  arctan    
5



2. Which graph shows y = cos-1(x)?
a)
b)
c)
d)
3. Which is an equation of the graph shown below?
a) y = arcsin(x)
b) y = arcos(x)
c) y = csc(x)
d) y = sec(x)
4. The function f(x) = sinx is defined in such a way that f
a) {x | 0  x   }
b) {x | 0  x  2 }
1
( x) is a function. What can be the domain of f(x)?
c) {x | 

2
x

2
}
d) {x | 
5. In order for its inverse to be a function, the domain of y =cosx must be restricted quadrants
a) I and II
b) II and IV
c) III and IV
d) I and IV
6. a) Graph the function y = arccos(x) being sure to label all necessary information.
b) Identify the domain and range of the function
y
x

2
x
3
}
2