Q. 101 - Precalculus Enhanced with Graphing Utilities

Question

Explain the term amplitude as it relates to the graph of a sinusoidal function. 

Step-by-Step Solution

Answer

The amplitude of a sinusoidal function represents the range of the sinusoidal function.

Step 1. Concept Used

If $\omega >0$, then the amplitude and period of $y=A\sin \left(\omega x\right)$ and $y=A\cos \left(\omega x\right)$ are given by

Amplitude$=\left|A\right|$

Period$=\frac{2\mathrm{\pi }}{\omega }$

Step 2. Find what amplitude represents

The function of the form $y=A\sin x$ is called a sinusoidal function and its amplitude is given as $\left|A\right|$.

The amplitude represents the distance between the center line of the function  and the top or bottom of the function.

The amplitude gives the range of the function. 

For the function $y=A\sin \left(\omega x\right)$ the graph will lie between $-A$ to $A$ in the $y$-axis.