Q 22. - Precalculus Enhanced with Graphing Utilities

Question

Match the given function to one of the graphs.

$y=2\cos \left(\frac{\mathrm{\pi }}{2}x\right)$.

Step-by-Step Solution

Answer

The correct option is (E). The graph is 

Step 1. Given Information.

Match the given function to one of the graphs.

$y=2\cos \left(\frac{\mathrm{\pi }}{2}x\right)$.

Step 2. Graphing Utility.

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

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

On comparing, we get

$A=2, \omega =\frac{\pi }{2}$

Period , $T=\frac{2\mathrm{\pi }}{{\displaystyle \frac{\mathrm{\pi }}{2}}}=4$.

The graph is