1. Inverse Trigonometric Functions
OBJECTIVES:
Evaluate the inverse trigonometric functions
Evaluate the compositions of trigonometric functions

2. Inverse functions
RECALL: for a function to have an inverse function, it must be one-to-one – that is, it must pass the Horizontal Line Test.
So consider the graphs of the six trigonometric functions, will they pass the Horizontal Line Test?

3. Inverse Trigonometric functions
However, if you restrict the domain of the trig functions, you will have a unique inverse function. But in such a restriction, the range will be unchanged, it will take on the full range of values for the trig function. Therefore, allowing the trig function to be one-to-one.
The INVERSE SINE FUNCTION is defined by
where the domain is and the range is

4. EX 1: If possible, find the exact value

5. Inverse Trigonometric functions
The INVERSE COSINE FUNCTION is defined by
where the domain is and the range is
The INVERSE TANGENT FUNCTION is defined by
where the domain is and the range is

6. EX 2: If possible, find the exact value

7. Inverse Trigonometric Functions
Domain
Range
Quadrant of the Unit Circle Range Values come from
I and IV
I and II

8. EX 3: Use a calculator to approximate the value, if possible

9. EX4: Find the exact value of the composition function

10. EX4: Find the exact value of the composition functionB)

11. EX4: Find the exact value of the composition function

12. EX4: Find the exact value of the composition function