Q. 38 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 35-38, find the amplitude, period, and phase shift of each function. Graph each function. Show at least two periods.

$y=-\frac{2}{3}\cos (\pi x-6)$

Step-by-Step Solution

Answer

The amplitude, time period , phase shift is $\frac{2}{3},2,\frac{6}{\mathrm{\pi }}$ respectively and the graph is 

Step 1: Given information

Given function $y=-\frac{2}{3}\cos (\pi x-6)$

Step 2: Comparing with y = A cos ( b x - ∅ ) + B and calculating

Comparing, we get

$$\begin{gathered} A=\frac{2}{3} \\ T=\frac{2\mathrm{\pi }}{\mathrm{\pi }} \\ T=2 \\ \frac{\varnothing }{\mathrm{\omega }}=\frac{6}{\mathrm{\pi }} \end{gathered}$$

Step 3: Sketching the graph

Sketching, we get