Question

Determine the amplitude and period of each function without graphing.

$y=2\sin x$.

Short answer

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

Step-by-step solution

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