Graphs of Sine and Cosine Objective: Students will be able to graph basic sine and cosine waves with transformations.

Sine Wave Remember you graph using the values from the unit circle Change the window on your calculator to adjust to radians or degrees

Exploration 1

Exploration 1

Cosine Wave

Basic Functions and Their Transformations When a is 1 you have a basic curve

The reciprocal of the function, number of cycles the wave completes in a unit interval, how long does it take to do the normal pattern of the graph Phase Shift – moving a graph left right up or down Where would you put a number to move it left and right The c value Where would you put a number to move it up or down The d value

Example

Example

Example What is the: Amplitude Period Frequency

Example

Example Think of the b(x-c) as a separate ( ) from original equation

Example

End Behavior

Example

Homework 13 and 14 find amplitude, period and frequency 29-34 49,50,57,58,75