1. Inverse Trigonometric Functions
Section 4.7
Inverse Trigonometric Functions

2. Objective By following instructions students will be able to:
Evaluate inverse sine functions.
Evaluate other inverse trigonometric functions.
Evaluate compositions of trigonometric functions.

3. Inverse Sine Function y= arc sin x
Recall: in order for a function to have an inverse, it must pass the horizontal line test.
iff
where: 1. 2.
3. Domain: [-1,1]
4. Range:

4. Example 1: Evaluating the Inverse Sine Function
If possible, find the exact value. a) b) c)

5. Example 2: Graphing the Arcsine Function
Sketch the graph of

6. Inverse Cosine Function
Y= arc cos x
Recall: in order for a function to have an inverse, it must pass the horizontal line test.
iff
where: 1. 2.
3. Domain: [-1,1]
4. Range:

7. Inverse Tangent Function
Y= arc tan x
Recall: in order for a function to have an inverse, it must pass the horizontal line test.
iff
where: 1. 2.
3. Domain:
4. Range:

8. Example 3: Evaluating Inverse Trigonometric Functions
Find the exact value. a) b) c) d)

9. Example 4: Calculators and Inverse Trigonometric Functions
If possible, use a calculator to approximate the value. a) b) c)

10. Compositions of Functions
Inverse Properties
If…
Then…
and

11. Example 5: Use Inverse Properties
If possible, find the exact value. a) b) c)

12. Example 6: Evaluating Composition of Functions
Find the exact value of… a) b)

13. Example 7: Some Problems from Calculus
Write each of the following as an algebraic expression in x. a) b)

14. Revisit Objective Did we… Evaluate inverse sine functions?
Evaluate other inverse trigonometric functions?
Evaluate compositions of trigonometric functions?

15. Homework
Pg 351 # 1-53 ALL