1. Trigonometric Inverses
Changing the domain
L. Marizza A. Bailey

2. Definition of Inverse Let Then f has an inverse g if and only if
Calculus Lesson 13
12/4/2018
Definition of Inverse
Let Then f has an inverse g if and only if
Then if and
is a function if and only if each y is assigned to only one x
L. Marizza A. Bailey

3. Definition of Inverse
is a function if and only if each y is assigned to only one x
This function is not invertible. This means it does not have and inverse

4. Definition of Inverse
is a function if and only if each y is assigned to only one x
This function is invertible. This means it does have and inverse

5. Sine is not invertible
The sine function is not invertible on the real line
If we change the domain to , then it will be invertible.

6. sin-1 (x) = arcsin(x) The domain of arcsin is the range of sin
The range of arcsin is the domain of sin
Note the domain and range

7. cos-1(x) = arccos(x) What is the domain of invertibility of cosine?
Write the cosine function with domain and range of invertibility?
Write the arccosine function with domain and range of invertibility?

8. The domain of invertibility of Sine
Which of these angles generates same y-coor?
Not in domain

9. The domain of invertibility of Cosine