Q 4. - Precalculus Enhanced with Graphing Utilities

Question

The function $y=A \sin \left(\omega x\right) , A>0$ has has amplitude 3 and period 2; then $A = \_\_\_\_\_\_ \& \omega =\_\_\_\_\_\_.$

Step-by-Step Solution

Answer

The function $y=A \sin \left(\omega x\right) , A>0$ has amplitude 3 and period 2; then $A = \_3\_\_ \& \omega = \_\_\pi \_.$

Step 1. Given Information.

The function $y=A \sin \left(\omega x\right) , A>0$ has amplitude 3 and period 2; then $A=\_\_\_\_, \omega =\_\_\_\_.$

Step 2. Filling Up.

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

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

The amplitude $\left|A\right|=3$.

The Period will be

 $$\begin{gathered} 2=\frac{2\mathrm{\pi }}{\omega } \\ \Rightarrow \omega =\pi \end{gathered}$$