Manipulation

Formula	Movement
`y = cos(x) - 1`	Vertical shift down by 1
`y = 2cos(x)`	Vertical stretch by a factor of 2
`y = -cos(x)`	Flip over x axis
`y = cos(2x)`	Horizontal shrink by a factor of 2

Periodic Functions

A function is considered periodic if it repeats itself at even intervals, where each interval is a complete cycle, referred to as a period.

A function that has the same shape as a sine or cosine wave is known as a sinusoidal function.

There are 4 general functions:

$$A * sin(B*x - C) + D$$	y = A * cos(B*x -c) + D$$
y = A * sin(B(x - \frac{C}{B})) + D	y = A*cos(B(x - \frac{C}{B})) + D$$

Variable	Meaning
`A`	The amplitude of a function can be found by taking `\\|A\\|`. The sign flips it over the x axis
`B`	Horizontal, or phase

 y = A * \sin(B(x-\frac{C}{B}))