Question

What is the amplitude and period of$y=-4\cos \left(\mathrm{\pi x}\right)?$

Short answer

The amplitude of$y=-4\cos \left(\mathrm{\pi x}\right)$is$A=4$and period is$P=2$

Step-by-step solution

Step 1. GIven data

The given function is

$y=-4\cos \left(\mathrm{\pi }x\right)$

Step 2. Amplitude

Compare the function with the standard cosine function

$$\begin{gathered} y=-A\cos \left(\varpi \theta \right) \\ y=-4\cos \left(\mathrm{\pi x}\right) \end{gathered}$$

So Amplitude$A=4$

Step 3. period

Period of function $y=A\cos \left(\varpi \vartheta \right)$is $\frac{2\mathrm{\pi }}{\varpi }$

Period of $y=-4\cos \left(\mathrm{\pi x}\right)$is

role="math" $$\begin{gathered} P=\frac{2\mathrm{\pi }}{\varpi } \\ P=\frac{2\mathrm{\pi }}{\mathrm{\pi }} \\ P=2 \end{gathered}$$

So period isrole="math" localid="1646860172855" $P=2$