Q 11. Given Information. - Precalculus Enhanced with Graphing Utilities

Question

Determine the amplitude and period of each function without graphing. 

$y=2\sin x$.

Step-by-Step Solution

Answer

The amplitude is $A=2$ and period is $2\mathrm{\pi }$.

Step 1. Given Information.

Determine the amplitude and period of each function without graphing. 

$y=2\sin x$.

Step 2. Evaluation.

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

Amplitude $=\left|A\right|$ 

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

On comparing, we get

$\omega =1$.

The amplitude is $A=2$.

The period is $T=\frac{2\mathrm{\pi }}{1}=2\mathrm{\pi }$.