Question

Determine the amplitude and period of each function without graphing.

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

Short answer

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

Step-by-step solution

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

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

$\omega =2$

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