1. Section 4.7 Inverse Trigonometric Functions
Remember that an inverse function is a function that “undoes” the original function.
A trig function maps an angle measure to a ratio.
An inverse trig function maps a ratio back to an angle measure.

2. Compare sin x with sin-1 x.
Notice that the domain
is [-1,1].
Notice that the range is

3. Compare cos x with cos-1 x.
Notice that the domain
is [-1,1].
Notice that the range is

4. Compare tan x with tan-1 x.
Notice that the domain is [-∞,∞].
Notice that the range is

5. Equivalent notations:
sin-1 x  arcsin x
cos-1 x  arccos x
tan-1 x  arctan x
By definition, answers to inverse trigonometric functions are always in radians.

6. Ex 1: Evaluate the following.
a. arcsin
b. sin-1
c. sin-1 2

7. Ex 2: Evaluate the following.
a. arccos b. cos-1 -1
c. tan d. arctan (-1)

8. Ex 3: Evaluate the following using a calculator.
a. arctan (-8.45) b. cos-1 2
c. sin-1 (0.2447)

9. Suggested Assignment:
Section 4.7
pg 316 – 317
#1 – 7, 13 – 24, 27 – 30