# What is the amplitude of a sinusoidal graph?

Jun 29, 2015

It is one-half of the difference between the maximum and minimum values of $y$.

#### Explanation:

Example: $y = - 7 \sin \left(3 x - 2\right) + 4$ has a maximum of $11$ and a minimum of $- 3$.
The amplitude is $\frac{1}{2} \left(11 - \left(- 3\right)\right) = \frac{1}{2} \left(14\right) = 7$

Note that the amplitude is the absolute value of the coefficient of $\sin \left(3 x - 2\right)$.

Here is the graph of the example:

graph{y=-7sin(3x-2) + 4 [-20.15, 20.4, -7.78, 12.5]}