4.4 Trigonometric 4.4 Trigonometric Functions of Any Functions of Any

AngleAngle

Let be an angle in Standard position and (x,y) on the terminal side

Let r ≠ 0

22 yxr

x

yTan

r

xCos

r

ySin

y

xCot

x

rSec

y

rCsc

Let (-5,12) be a point on the terminal side of

Find the Sin, Cos and Tan

5

12

13

5

13

12

Tan

Cos

Sin

13169

125 22

r

r

Tan

Cos

Sin

Tan

Cos

Sin

Tan

Cos

Sin

Tan

Cos

Sin

Reference Angles

What is the value of Sin 30º and Sin 150º ?

'

Reference Angles

What is the value of Sin 30º and Sin 150º ?

Why not just use Sin 30º

Good news you can,

30º is the reference angle for 150º

But Cos 30º ≠ Cos 150º;

How are they related?

'

Reference Angles

How to find a Reference Angle.

All reference angles are

During a Code Blue you need to get into the closest classroom; the reference angle is the closest angle to 180º or 360º.

'

2'0

Reference Angles

Finding the reference angle

What is the reference angle of 110º ?

What is the reference angle of 284º ?

What about 72º ?

'

Reference Angles

Finding the reference angle

What is the reference angle of ?

What is the reference angle of ?

What about 1.8 radians ?

'

4

5

3

5

What is the exact value of Sin

What is the reference angle of

4

7

4

7

What is the exact value of Sin

What is the reference angle of

What is

4

7

4

7

4

4

Sin

What is the exact value of Sin

What is the reference angle of

What is

What Quadrant is in ?

4

7

4

7

4

2

2

4

Sin

4

7

What is the exact value of Sin

What is the reference angle of

What is

What Quadrant is in ?

So

4

7

4

7

4

2

2

4

Sin

4

7

2

2

4

7

Sin

Find Sec

What is the coterminal angle with ?

What quadrant is in?

4

11

4

11

4

4

32

4

11

4

11

Find Sec

So the we need to find

4

11

22

22

2

2

2

2

1

4cos

1

24

11

Sec

Using Trigonometric IdentitiesGiven: Find

22

3

3

2

and

Cos

Tan

and

Sin

9

5sin

1sin9

4

1sin3

2

2

2

22

3

5sin

9

5sin

Using Trigonometric IdentitiesGiven: Find

22

3

3

2

and

Cos

Tan

and

Sin

9

5sin

1sin9

4

1sin3

2

2

2

22

3

5sin

9

5sin

2

5

3235

Tan

HomeworkHomework

Page 297 – 299Page 297 – 299

##3, 9, 16, 22, 3, 9, 16, 22,

28, 34, 40 ,46, 28, 34, 40 ,46,

52, 58, 64, 74, 52, 58, 64, 74,

82, 90, 96 82, 90, 96

HomeworkHomework

Page 297 – 299Page 297 – 299

## 6, 13, 19, 25, 6, 13, 19, 25,

31, 37, 43, 49, 31, 37, 43, 49,

55, 61, 70, 78, 55, 61, 70, 78,

86, 94, 9786, 94, 97