PAP Precalculus
Inverse Trigonometric Functions
Inverse Trig Functions – Finding Angles
y = sin(x)
y = arcsin(x)
y
Domain:
4
3
Range:
2
1
x
-3 /2
-
- /2
/2
3 /2
π/2
-1
-2
-3
-4
-π/2
y = cos(x)
y
y = arccos(x)
4
3
Domain:
2
1
x
-3 /2
-
- /2
/2
Range:
3 /2
-1
-2
-3
-4
π
0
y = tan-1 (x)
y = arctan(x)
Domain:
Range:
π/2
-π/2
Rules:
y = arcsin(x) if sin(y) = x
y = arccos(x) if cos(y) = x
y = arctan(x) if tan(y) = x
x----------x----------x----------x----------x----------x--------x
If possible, find the exact value in radians (no decimals). Use the restricted domain.
1 
1

2
1) arcsin (-1)

4) arcsin  

1
2) sin 
3

2 

5) arccos  

3) sin (
3

2 
2
)
2
6) tan-1 (-1)
[0,2 )
 3
8) cot x  

 3 
For #7-12, find all exact radian values from
7) tan x = (1)
10)
cos x  (1)

11) sin x   

9) tan x = (0)
2

2 
12) cos x = (0)
If possible, find the exact value. Use the restricted domain.
13)
tan  arctan(0)

15) sin  arcsin

 3

2 

 3 

2

 
14) cos arcsin 


 1 

 2 
16) cos arccos  
