Q 15. - Precalculus Enhanced with Graphing Utilities

Question

Determine the amplitude and period of each function without graphing. 

$y=6\sin \left(\mathrm{\pi x}\right)$.

Step-by-Step Solution

Answer

The amplitude is 6 and period is 2.

Step 1. Given Information.

Determine the amplitude and period of each function without graphing. 

$y=6\sin \left(\mathrm{\pi x}\right)$.

Step 2. Evaluation.

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

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

On comapring, we get

$\left|A\right|=6$ , $\omega =\pi$

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