6.3

Graphing Sine and Cosine Functions

Periodic Functions

• A periodic function is a function with a repeating pattern this includes sin and cos graphs.

• How long does it take for the graph to repeated itself?

360 ( for degrees) OR 2 (for radians)

Periodic Functions

• A periodic function f exists if there is a positive constant p so:

f (s+p ) = f (s)

P is the period (provided it is the least possible value)

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

-1.0

-0.8

-0.6

-0.4

-0.2

0.2

0.4

0.6

0.8

1.0

x

y

y = sinx

Characteristics of the Sine Function

1. The domain is the set of all real numbers.

2. The range consists of all real numbers from -1 to 1, inclusive.

3. The sine function is an odd function (symmetric with respect to the origin).

4.

Characteristics of the Sine Function

5.

6.

Ex.

• Find the value of 9pi/2 by using the graph of the sine function.

• Find the values of theta for which – sin(theta) = 0 is true

Graph y = sin(x) from 3pi to 5pi

0 2 4 6

1.5

1.5

(0, 1)

Characteristics of the Cosine Function

1. The domain is the set of all real numbers.

2. The range consists of all real numbers from -1 to 1, inclusive.3. The cosine function is an even function (symmetric with respect to the y-axis).

4.

5.

Characteristics of the Cosine Function

6.

The graphs of the sine and cosine functions are called sinusoidal graphs.

Ex:

• #33 on p.364

• Graph y = cos(x) from -5pi to -3pi inclusive