Section 5.5 Graphs of Sine and Cosine Functions

The Graph of y=sin x

Continuation of the previous problem showing 3 cycles

Graphing Variations of y=sin x

Graphing y=2 Sin x

Graphing y=½ Sin x

Graphing y=-2 Sin x

Graphing y=3 Sin 2x

The Effect of Horizontally Shifting the Graph

Example

Example

Example

Example

Example

Example

The Graph of y=cos x

Graphing Variations of y= cos x

Cosine with a Different Amplitude and Period

Example

Example

Vertical Shifts of Sinusoidal Graphs

Cosine Function with a Vertical Shift

Example

Example

Modeling Periodic Behavior

Example 20 10 2 6 10 14 18 22 26 The number of hours after midnight.

(a) (b) (c) (d)

(a) (b) (c) (d)

(a) (b) (c) (d)