Question

Determine the amplitude and period of each function without graphing.

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

Short answer

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

Step-by-step solution

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