Q 7. - Precalculus Enhanced with Graphing Utilities

Question

True or False For $y=2\sin \left(\mathrm{\pi x}\right)$, the amplitude is 2 and the period is $\frac{\mathrm{\pi }}{2}$. 

Step-by-Step Solution

Answer

False.

Step 1. Given Information.

True or False For $y=2\sin \left(\mathrm{\pi x}\right)$, the amplitude is 2 and the period is $\frac{\mathrm{\pi }}{2}$. 

Step 2. True or False.

For $y=2\sin \left(\mathrm{\pi x}\right)$ the amplitude is 2 and the period is $\frac{\mathrm{\pi }}{2}$.

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

Amplitude $=\left|A\right|$ , Period $=T=\frac{2\mathrm{\pi }}{\omega }$.

Here , on comparing we get,

$\omega =\pi$

Then, $T=\frac{2\mathrm{\pi }}{\mathrm{\pi }}=2$.

So, statement is false.