1. Inverse Sine, Cosine, and Tangent
Functions
*One-to-One Function
6.1 Inverse Trigonometric
Functions

2. Function and One-to-One
Function One-to-one
 For each x, there is
exactly one y.
 The graph “passes”
the vertical line test.
 For each y, there is
exactly one x.
 The graph “passes”
the horizontal line
test.
 If a function is one-to-
one, the inverse will
also be a function.

3. Inverse -
 The relation obtained by interchanging the x and
y values of a function.
 The inverse of a function that is NOT one-to-one
can be made a function by limiting the domain of
the original function to make it one-to-one.
 The domain of a function is the range of its
inverse.
 The range of a function is the domain of its
inverse.

4. Graph 2 2siny x x 
  
-2 -1
2
1
-2
-1
21
1
siny x


5. Graph cos 0y x x   
-1 4321
3
-1
2
1
1
cosy x


6. Graph 2 2tany x x 
  
-2 -1
2
1
-2
-1
21
1
tany x


7. Evaluate – exact value
 1 1
2sin

8. Evaluate – exact value
 1 2
2sin 

9. Evaluate – exact value
 1
cos 0

10. Evaluate – exact value
 1 1
2cos


11. Evaluate – exact value
 1
tan 1

12. Evaluate – exact value
 1
tan 3


13. Evaluate - approximation
1
sin 0.37
 1
cos 0.82

 1
tan 4.21

0.38
2.53
1.34 

14. 1 3
2cos cos
 
 
1
6sin sin  
  

15. 1
cos cos 0.75
  
1
9sin sin 
  

16. p. 457 # 1 - 4, 13 - 44
Assignment