Q 13. - Precalculus Enhanced with Graphing Utilities

Question

Determine the amplitude and period of each function without graphing. 

$y=-4\cos \left(2x\right)$.

Step-by-Step Solution

Answer

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

Step 1. Given Information.

Determine the amplitude and period of each function without graphing. 

$y=-4\cos \left(2x\right)$.

Step 2. Evaluation.

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

Amplitude $=\left|A\right|$ and period $=T=\frac{2\mathrm{\pi }}{\omega }$.

On comapring, we get

$A=\left|-4\right|=4$

$\omega =2$

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