Question

Determine the amplitude and period of each function without graphing.

$y=\frac{9}{5}\cos \left(-\frac{3\mathrm{\pi }}{2}x\right)$.

Short answer

The amplitude is $\frac{9}{5}$and period is$\frac{4}{3}$.

Step-by-step solution

Step 1. Given Information.

Determine the amplitude and period of each function without graphing.

$y=\frac{9}{5}\cos \left(-\frac{3\mathrm{\pi }}{2}x\right)$.

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

On comparing, we get

Amplitude $=\left|\frac{9}{5}\right|=\frac{9}{5}$, $\omega =-\frac{3\mathrm{\pi }}{2}$

Then, Period$=T=\frac{2\mathrm{\pi }}{-{\displaystyle \frac{3\mathrm{\pi }}{2}}}=-\frac{4}{3}$.