Class Work

1. Find the exact value of cot 330

2. Find sin2x, cos2x, and tan2x given tan x = -3/2 and 90 < x< 180

Class Work

3. Find and 180 < x < 2702

sin sin2 3

ugiven u

Section 7.4Inverse Trigonometric Functions

Objectives:•To define the inverse of the sine, cosine, and tangent functions.•To understand the domain and range of the inverse trig functions.

Inverse Sine FunctionThe inverse of the function sin is the function

sin–1 defined by: sin–1x = y sin y = xfor –1 ≤ x ≤ 1 and –π/2 ≤ y ≤ π/2.

Example 1. Find the exact value of the expression if it is defined:

(a)sin–1 ½

(b)sin–1 (–½)

(c)sin–1 (3/2)

Class Work Find the exact value of the expression if it is

defined:4.

5.

1 2sin

2

1 5sin4

Inverse Cosine FunctionThe inverse cosine function is the function cos–1 with domain [–1, 1] and range [0, π], defined by:

cos–1 x = y cos y = x

Ex 2. Find the exact value of the expression if it is defined:

(a) cos–1

b) cos–1 0

c) cos–1 (5/7)

( 3 / 2)

Class WorkFind the exact value of the expression if it is

defined:6.

7.

1 2cos

2

1cos ( 1)

Inverse Tangent FunctionThe inverse tangent function is the function tan–1 with domain and range (–π/2, π/2) defined by:

tan–1 x = y tan y = x

Ex 3. Find the exact value of the expression if it is defined:

(a)tan–1 1

(b)tan–1

(c)tan–1(–20)

3

Class WorkFind the exact value of the expression if it is

defined:

8.

9.

1tan ( 1)

1 3tan

3

Ex 4. Find the exact value of the expression, if it is defined.

a.)

b.)

c.)

1sin (sin )4

1tan(tan 5)

1cos cos3

Class WorkFind the exact value of the expression, if it is

defined.

10.

11.

1sin sin6

1 2tan tan

3

Ex 5. Find the exact value of the expression, if it is defined.

a.)

b.)

c.)

1 2sin cos

3

1 1tan sin2

1 5sin cos

6

Class Work

Find the exact value of the expression, if it is defined.

12.

13.

1 1tan sin2

1 3cos sin

4

HW#4 p557 1,4,6,7,10,11,13,16,18,

21,26,53,54