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
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