# How do you determine the amplitude of y= 5 sin x and y= 3 cos x?

Apr 25, 2015

Both $\sin \left(x\right) \text{ and } \cos \left(x\right)$ have a Range of
$\left[- 1 , + 1\right]$

$y = 5 \sin \left(x\right)$
maps the points of $\sin \left(x\right)$ into a stretched Range of
$\left[- 5 , + 5\right]$
and thus an amplitude of $5$.

Similarly
$y = 3 \cos \left(x\right)$
has an amplitude of $3$