Unit 5

x sin x -π 0

2

-1

0 0

6

0.5

3

0.866

2

1

π 0

2

3 -1

2π 0

2

5 1

3π 0

y = sin x

π

1

-1

x cos x -π -1

2

0

0 1

6

0.866

3

.5

2

0

π -1

2

3 0

2π 1

2

5 0

3π -1

y = cos x

π

1

-1

1. Amplitude of a Sine Wave

Graph y1 = sin(x) and y2 = 2 sin(x) on the axes provided.

2 4 -4 -2

2

1

-1

-2

0

0

x

y

Amplitude of a Sine Wave

The amplitude of a sine wave is one-half the difference between the highest and lowest value of y.

||cos

sinAamplitude

xAy

xAy

2. Period of a Sine Wave

Graph y1 = sin(x) and y2 = sin(2x) on the axes provided.

2 4 -4 -2

2

1

-1

-2

0

0

x

y

Period of a Sine Wave

The period of a sine wave is the distance between wave peaks.

bperiod

bxy

bxy 2

cos

sin

5.5 – Graphs of Sine and Cosine The standard form of the sine and cosine equations are:

dcxbay sin , dcxbay cos Where:

│a│ is the amplitude

b

2 is the period

c/b is the phase shift (or horizontal shift) d is the vertical shift

Examples: Sketch the following by hand:

1.

2sin3

xy

Amp = Period =

π

1

-1

Examples: Sketch the following by hand:

2. xy 3sin2

1

Amp = Period =

π

1

-1

Examples: Sketch the following by hand:

3.

3cos2

xy

Amp = Period =

π

1

-1

Examples: Sketch the following by hand:

4. xy 4cos3

1

Amp = Period =

π

1

-1

» Graphing Worksheet