Find the exact values:

2cot

3

7csc

4

5cos

6

2sin

3

17tan

6

sec2

3

3

2

2

3

2

3

3

3

undefined

Inverse Trig Functions

Inverse: “the angle whose (trig function) is x”

Arcsin x or [-90° to 90°]

Arccos x or [0° to 180°]

Arctan x or (-90° to 90°)

1sin x

1cos x

1tan x

I wonder why the above inverses are limitedto the different domains above……let’s explore.

Recall that for a function to have an INVERSE function, it must be one-to-one.

In other words, it must pass the Horizontal Line Test.

Let’s see why Inverse Sine has a restricted domain…….

onetooneis

valuesofrangefullontakes

INCREASINGisfunction

truearefollowingThe

)3

)2

)1

:

When evaluating the inverse sine function, it helps to remember the phrase “the arcsine of x is the angle (or number) whose sine is x.”

1 1sin

2

The angle you are looking for MUST give a POSITIVE answer for sine. Therefore, we mustbe in Quadrant I.

+

-

Evaluate

2

1sin 1 Must be in Q4.

Possible Answers:

Evaluate:

arcsin(1)

1arccos

2

+-

902or

+

-

603or

Evaluate:

1tan ( 3)

arctan 3

+

-

603or

603

or

Evaluate:

arcsin(2)

1tan arcsin

2

undefined

6

tan

3

3

Evaluate:

1 1sin cos

2

1cos arcsin

2

3

sin 2

3

6

cos 2

3

Evaluate:

1 12 2tan sin cos

2 2

0

0tan

44tan

Evaluate:

1 1 1sin sin 1 cos

2

2

1

6sin

6

2

6

3sin

32sin

2

1

30sin

6090sin

Evaluate:

1 5tan sin

13

Not on the Unit Circle – MUST DRAW!

513

12

Homework

Inverse Trig worksheet