Trig – Section 4Graphing Sine and Cosine

Objectives: •To graph sine and cosine curves•To find amplitude, period and phase shifts.

Sine Curve:

(1,0)

(0,1)

(-1, 0)

(0,-1)

02

2

3

2

1

-1

2

3

2

2

Ex 1. Graph the following functions.

a) y = -sin x

b) y = ½ sin x 1

-12

3

2

2

1

-12

3

2

2

c) y = 1 + sin x

d) y = 2sin x1

-12

3

2

2

1

-12

3

2

2

Cosine Curve:

(1,0)

(0,1)

(-1, 0)

(0,-1)

02

2

3

2

1

-1

2

3

2

2

Ex 2. Graph the following functions.

a) y = cos x

b) y = 2 + cos x

1

-12

3

2

2

1

-12

3

2

2

c) y = -3cos x

1

-1

2

3

2

2

Class Work1. Graph y = 1 – sin x

2. Graph y = -1 + cos x

3. Graph 1sin2

y x

Amplitude and Period of Sine and Cosine Curves:

Ex 3. Find the amplitude and period of each function.

a)

b)

c)

4cos3y x

12sin

2y x

5cos3

y x

Shifted Sine and Cosine Curves:

The sine and cosine curves

have amplitude of , period , and

phase shift b.

sin ( ) cos ( )y a k x b and y a k x b

a2

k

Find the amplitude, period, and phase shift of the following.

a)

b)

c)

3sin 24

y x

2cos 43

y x

1 5sin8 1.3y x

Class WorkFind the amplitude period and phase shift of the following.

4.

5.

2 34sin

3 4y x

1 114cos

6 6y x

HW #6Graphing Worksheet

HW #7 Amplitude, Period, and Phase Shift

Worksheet All