Q 16. - Precalculus Enhanced with Graphing Utilities

Question

Determine the amplitude and period of each function without graphing. 

$y=-3\cos \left(3x\right)$.

Step-by-Step Solution

Answer

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

Step 1. Given Information.

Determine the amplitude and period of each function without graphing. 

$y=-3\cos \left(3x\right)$.

Step 2. Evaluation.

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

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

On comparing, we get

$\left|A\right|=\left|-3\right|=3 , \omega =3$

then, $T=\frac{2\mathrm{\pi }}{3}$.