7.5 The Other Trigonometric Functions

7.5 THE OTHER TRIG FUNCTIONS

Objectives: Evaluate csc, sec and cot

Vocabulary: Cosecant, Secant, Cotangent

Right Triangle Trig. FunctionsLet be an acute angle of a right triangle.

If is a second quadrant angle and sin is 3/5, find the remaining five functions.

7.5 THE OTHER TRIG FUNCTIONS

Find the six trig functions for: 330°

7.5 THE OTHER TRIG FUNCTIONS

x

Find the six trig functions of 330o .

Second, find the reference angle, 360o – 330o = 30o

[Solution] First draw the 330o angle.

To compute the trig functions of the 30o angle, draw the “special” triangle or recall from the table.

Determine the correct sign for the trig functions of 330o . Only the cosine and the secant are “+”.

AS

T C

330o30o

1sin 330 sin 30 csc330 2

2

3 2 2 3cos330 cos30 sec330

2 33

3 3tan 330 tan 30 cot 330 3

3 3

[Solution] The six trig functions of 330o are:

Find the six trig functions of 330o .

Find the six trig functions for:

7.5 THE OTHER TRIG FUNCTIONS

AS

T C

Find the six trig functions of . 3

4

y

x

3

4

3

3

3

3

1

3

4cot3

3

4tan

23

4sec

2

1

3

4cos

3

32

3

2

3

4csc

2

3

3

4sin

Before we write the functions, we need to determine the signs for each function. Remember “All Students Take Calculus”. Since the angle, , is located in the 3rd quadrant, only the tangent and cotangent are positive. All the other functions are negative..

3

4

Find the six trig functions for:

7.5 THE OTHER TRIG FUNCTIONS

0 radians

Find the six trig functions for .

We will first draw the angle to determine the quadrant.

AS

T CWe know that is the same as 45 , so the reference angle is 45 . Using the special triangle.

4

Note that the reference angle is .

4

4

13

4

4

2

4

4

4

64

5 4

7

4

8

4

94

10

4

114

3

We see that the angle is located in the 3rd quadrant.

4

13

4

12

4

13

4

13 1 2 13 2sin csc

4 2 4 12

13 1 2 13 2cos sec

4 2 4 1213 1 13 1

tan 1 cot 14 1 4 1

TB p. 286#13-27 odd skip 19 & 21

7.5 THE OTHER TRIG FUNCTIONS