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### Graphing Trig Functions

Posted: June 1st, 2011, 9:02 pm
Graphing Sine and Cosine

Sine function: $y = \sin{x}$

Cosine function: $y = \cos{x}$

The amplitude of $y = a \sin{x}$ and $y = a \cos{x}$ represents half the distance between the maximum and minimum values of the function and is given by

Amplitude = $\left | a \right |$

$y = d + a \sin(bx - c)$

$y = d + a \cos(bx - c)$

a = vertical stretch/shrink amplitude
b = horizontal stretch/shrink period
c = move left or right phase shift
d = move up or down

Period of Sine and Cosine function:

$\frac{2\pi}{b}$

Other info:

X-scale = $\frac{period}{4}$
Phase shift = $\frac{-c}{d}$

If a is negative, there is an x-axis reflection