Question

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

Short answer

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

Step-by-step solution

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.