3.2 The Inverses Continued

Warm-up (IN)1. What is the domain and range of

?

2. True or False: The graph of is

increasing on the interval and .

3. If and , then ____?

Learning Objective: To identify and understand the procedure of solving more involved inverse expressions, to understand the limitations of cot, csc, and sec inverse functions, and to be able to use the calculator to check your work.

secy x

secy x

0,2

,2

cot 2 0 cos

D: all real #s except odd multiples of R: 1y 2

True

2 5

5

NOTES

Ex 1 – Find the exact value of…

1 5a. sin sin

4

5sin

4

2

2

1 2sin

2

4

1 1b. sin tan

2

1tan

2

1

2

5

so...sin 1

5

5

5

1 1c. cos sin

3

1sin

3

1

3

2 2 so...cos 2 2

3

where is sin neg?

Quad III & IV

must be in IV

1 1d. tan cos

3

1

cos3

1

32 2

so...tan 2 2

where is cos neg?

Quad II & III

must be in II

Limits to inverses:

X

(values)

Y

(angles)

1cscy x 1x

2,

2

1secy x 1x ,0

1coty x , 0,

Except 0

Except 2

Find the exact value of Ex 2 -

1csc 2

must be between ,2 2

csc 2

12

sin

1sin

2 1 1

sin2

6

Approximate the value of each...Ex 3 - 1a. sec 3 sec 3 1

3cos

1cos

3 1.23rad

1b. csc 4 csc 4 1

4sin

1sin

4

.25rad

1 1c. cot

2 Cot and tan don’t have the same

range, so we can’t use tan…

What has the same range as cot??Cos!

1

25

So…we need to find out what cos is…

1cos

5 1.1rad

1d. cot 2

2

51

2cos

5

2.68rad

HW – pg. 236 #9-16,21-26,33-35,39-43

Out – Find

Summary – I think working with inverses can be difficult because…

Don’t forget about POW!!

1sin tan 1