# How do you find the amplitude and period of a function y = sin (pix - 1/2)?

Nov 7, 2015

Amplitude: 1
Period: 2

#### Explanation:

Sin functions are written on a common form:
$A \sin \left(b x + c\right) + d$

Where A signifies the amplitude ($\frac{\text{top value - bottom value}}{2}$)
b affects the frequency
c signifies the horisontal shift
d signifies the vertical shift

You can find the amplitude by looking at the coifficient before $\text{sin}$. In this case, the amplitude is 1.

The period is defined by $\frac{2 \pi}{b}$
In this case: $\frac{2 \pi}{\pi} = \frac{2 \cancel{\pi}}{\cancel{\pi}} = 2$