Q 14. - Precalculus Enhanced with Graphing Utilities

Question

Determine the amplitude and period of each function without graphing. 

$y=-\sin \left(\frac{1}{2}x\right)$.

Step-by-Step Solution

Answer

Amplitude is 1 and period is $4\mathrm{\pi }$.

Step 1. Given Information.

Determine the amplitude and period of each function without graphing. 

$y=-\sin \left(\frac{1}{2}x\right)$.

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 comparing, we get

$A=\left|-1\right|=1$.

$\omega =\frac{1}{2}$, then

$T=\frac{2\mathrm{\pi }}{{\displaystyle \frac{1}{2}}}=2\mathrm{\pi }\times 2=4\mathrm{\pi }$.