# What is the amplitude of the function y=-3sin x?

Nov 26, 2014

The amplitude of $y = - 3 \sin x$ is 3.

graph{y=-3*sinx [-10, 10, -5, 5]}

Amplitude is the height of a periodic function, aka the distance from the center of the wave to it's highest point (or lowest point). You can also take the distance from the highest point to the lowest point of the graph and divide it by two.

$y = - 3 \sin x$ is the graph of a sinusoidal function. As a refresher, here's a breakdown of the general form you'll see sinusoidal functions in, and what the parts mean:

$y = A \cdot \sin \left(B \left(x - C\right)\right) + D$

$| A |$ = amplitude
$B$ = number of cycles from 0 to $2 \pi$
$D$ = vertical shift (or displacement)
$C$ = horizontal shift

We can recognize that the function $y = - 3 \sin x$ fits this format, where $A = - 3$, $B = 1$, $C = 0$ and $D = 0$. Changing the value of A will either stretch or shrink the graph. Remember, amplitude is a measure of distance and therefore is always positive.