Section 4.4Trigonometric Functions

of Any Angle

Trigonometric Functions

of

Any Angle

Example

0

0

0

0

Evaluate the cosine function and the cotangent function

at the following four quadrantal angles:

a. =0 0

b. 902

c. =180

3d. =270

2

The Signs of the Trigonometric Functions

Example

Name the quadrant in which lies if the cotangent

is positive and the sine is negative.

Example

4Given that cot = and sin >0 find the following:

3sin =

cos =

sec =

csc =

Reference Angles

Example

Find the reference angle, ', for each of the following

angles:

4

3

7

6

= - 120

Example

0

Find the reference angle, ', for each of the following

angles:

7

3

13

6

= 405

Evaluating Trigonometric Functions Using Reference

Angles

1

1

2

1

2

3

345

45 30

60

Find the sine, cosine and tangent of 30, 45 and 60 degree angles.

Here are the answers to the previous slide

Example

Use the reference angles to find the exact value of

each of the following trigonometric functions:

4sin

3

7cos

6

tan - 120

Example

0

Use the reference angles to find the exact value of

ech of the following trigonometric functions:

7sec

3

13csc

6

cot 405

(a)

(b)

(c)

(d)

0Find the reference angle for the angle -150

0

0

0

0

510

210

30

60

(a)

(b)

(c)

(d)

Use the reference angle to find the exact value of the

5following trigonometric function. csc

3

22

11

2

3

2

2 3

3