Section 4.5 Graphs of Sine and Cosine

Key Terms Amplitude (meters) The height of the wave or distance from the midline to the max/min. Period (seconds/ Radians) The time it takes to complete one cycle/wave. Frequency (Hertz or cycles per second, CPS) The number of waves in a given period of time. Midline (meters) The horizontal line in the middle of the wave. The average of the max and min. Y= (max+min)/2

The Graph of y=sin θ http://www.mathopenref.com/triggraphsine.html

3 cycles of Sin graph Graph begins at origin and goes up first (Dueling Dragons ) Domain= Range = Period= Even, odd, or neither=

Graphing Sinusoidal Graphs Parent Function y= sin x Transformations y= A sin (Bx –C) +D Parent Function y= cosx Transformations y= A cos (Bx –C) +D

Graphing sin Parent Function y= sin x Transformations y= A sin (Bx –C)

Graphing y=2 Sin x Graphing y=½ Sin x Graphing y=-2 Sin x

Graphing y=3 Sin 2x

Horizontal Shift of Sine *Highlight key points

Example

Example

Example

Example

Example

Example

The Graph of y=cos x http://www.mathopenref.com/triggraphcosine.html

Graphing Variations of y= cos θ Cosine with a Different Amplitude and Period * Starts at the top and goes out and down (The Hulk)

Horizontal Shift of Cosine

Example

Example

Vertical Shifts Example

Example

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

QUICK POLL (a) (b) (c) (d)

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

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