1 8.1 Inverse Trigonometric Functions In this section, we will study the following topics: Definitions of the inverse trig functions Evaluating inverse.

1

8.1 Inverse Trigonometric Functions

In this section, we will study the following topics:

Definitions of the inverse trig functions

Evaluating inverse sine, cosine, and tangent functions by hand and using the calculator.

2

3

4

5

6

7

8

9

Summary of the Inverse Trig Functions

Function Domain Range

1

1

1

sin sin 1 12 2

cos cos 1 1 0

tan tan2 2

y x iff x y x y

y x iff x y x y

y x iff x y x y

10

Evaluate the following inverse trig functions without using the

calculator. Give the exact answer in radians, in terms of .

1 111. sin 2. sin 1

2

Examples

11

1 1 23. cos 0 4. cos

2

Evaluate the following inverse trig functions without using the

calculator. Give the exact answer in radians, in terms of .

Examples

12

1 15. tan 1 6. tan 3

Examples

Evaluate the following inverse trig functions without using the

calculator. Give the exact answer in radians, in terms of .

13

Evaluate the following inverse trig functions using the

calculator. Give your answer in degrees, to the nearest tenth.

1 137. tan 8. sin 2.64

4

Examples

14

1 1 59. cos 0.15 10. tan

2

Examples

Evaluate the following inverse trig functions using the

calculator. Give your answer in degrees, to the nearest tenth.

15

Example

End of Section 8.1

16