# What is the period and amplitude for y=2 sin x?

Jun 11, 2015

The general formula for $\sin x$ is:

$A \sin \left(k x + \phi\right) + h$

$A$ is the amplitude
$k$ is some coefficient
$\phi$ is the phase shift or horizontal shift
$h$ is the vertical shift

$y = 2 \sin x$ lines up to be $A = 2$, $k = 1$, $\phi = 0$, and $h = 0$.

The period is defined as $T = \frac{2 \pi}{k}$, so therefore, the period is just $2 \pi$. The amplitude, of course, is $2$, since $A = 2$.