Q 12. - Precalculus Enhanced with Graphing Utilities

Question

Determine the amplitude and period of each function without graphing. 

$y=3\cos x$.

Step-by-Step Solution

Answer

The amplitude is 3 and period is $T=2\mathrm{\pi }$.

Step 1. Given Information.

Determine the amplitude and period of each function without graphing. 

$y=3\cos x$.

Step 2. Evaluation.

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

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

On comparing, we get

Amplitude $\left|A\right|=3$.

Then, $\omega =1$

Period $=T=\frac{2\mathrm{\pi }}{1}=2\mathrm{\pi }$.