Question

Determine the amplitude and period of each function without graphing.

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

Short answer

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

Step-by-step solution

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,$T=\frac{2\mathrm{\pi }}{3}$.