Graphs of Sine and Cosine

When thinking of the graphs of sine and cosine, refer to the Unit Circle.

Graph of 


Characteristics of a Sine Graph:

• Sine is an odd function:  -f(x) = f(-x) 
• Symmetry about the origin - for every (x,y) there is a (-x,-y)
• y-intercept = (0,0) (unless shifted) - Due to the  on the Unit Circle

Graph of 


Characteristics of a Cosine Graph:

• Cosine is an even function:  f(-x) = f(x)
• Symmetry about the y-axis - for every (x,y) there is a (-x,y)
• y-intercept is (0,1) (unless shifted) - Due to the  on the Unit Circle

Period of Sine and Cosine Functions:
The periods of sine and cosine functions are found by 
Why?
Using the unit circle, one cycle is  radians, therefore the distance over one cycle of a sine or cosine function would be a fraction of the circle itself.

Variables affect on Sine and Cosine Equations:
Equation: 

What does each variable do to the parent graph of  ?
a: Amplitude of the equation - a vertical stretch or compress
b: Changes the Period of the function - horizontal stretch or compress
c: Phase shift - a shift left or right on the x-axis
d: Vertical shift - up or down on the y-axis