Q. 39 - Precalculus Enhanced with Graphing Utilities

Question

Explain how the amplitude and period of a sinusoidal graph

are used to establish the scale on each coordinate axis.

Step-by-Step Solution

Answer

$y=A\sin \left(\omega x+\varnothing \right)$ determines the amplitude as well as time period of a sinusoidal graph.

Step 1. Given

A sinusoidal function.

Step 2. Calculation

$y=A\sin \left(\omega x+\varnothing \right)$

represents the sinusoidal function where A is the amplitude and since for $Sinx$ the maximum and minimum value will be $\pm 1$.

Therefore here it will be $\pm A$ which will be represented on y axis.

The time period is represented on x-axis.