Q. 34 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 33 and 34 , determine the amplitude and period of each function without graphing.

$y=-2\cos \left(3\pi x\right)$

Step-by-Step Solution

Answer

The amplitude and time period is $-2,\frac{2}{3}$ respectively

Step 1: Given information

Given function $y=-2\cos \left(3\pi x\right)$

Step 2: Compare with standard form and calculate

Comparing with $y=A\cos bx$, we get

$$\begin{gathered} A=-2 \\ T=\frac{2\mathrm{\pi }}{3\mathrm{\pi }} \\ T=\frac{2}{3} \end{gathered}$$