Q 5. - Precalculus Enhanced with Graphing Utilities

Question

The function $y=3 \cos \left(6x\right)$ has amplitude _______ and period _____.

Step-by-Step Solution

Answer

$$\begin{gathered} \left(a\right) 3 \\ \left(b\right) \frac{\mathrm{\pi }}{3} \end{gathered}$$.

Step 1. Given Information.

The function $y=3 \cos \left(6x\right)$ has amplitude _____ and period ______.

Step 2. Filling Up.

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

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

On Comparing $y=3\cos \left(6x\right)$, we get

$\left|A\right|=3$

Period $=T=\frac{2\mathrm{\pi }}{6}=\frac{\mathrm{\pi }}{3}$.