Q 19. - Precalculus Enhanced with Graphing Utilities

Question

Determine the amplitude and period of each function without graphing. 

$y=\frac{5}{3}\sin \left(-\frac{2\mathrm{\pi }}{3}x\right)$.

Step-by-Step Solution

Answer

The amplitude is $\frac{5}{3}$ and period is $-3$.

Step 1. Given Information.

Determine the amplitude and period of each function without graphing. 

$y=\frac{5}{3}\sin \left(-\frac{2\mathrm{\pi }}{3}x\right)$.

Step 2. Evaluation.

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

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

On comparing, we get

Amplitude $=\left|\frac{5}{3}\right|=\frac{5}{3} , \omega =-\frac{2\mathrm{\pi }}{3}$.

Period $T=\frac{2\mathrm{\pi }}{-{\displaystyle \frac{2\mathrm{\pi }}{3}}}=-3$.