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Chapter 6: Q. 63 (page 410)

Find an equation for each graph.

Short Answer

Expert verified

Equation for the graph is:

y=±5cosπ4x

Step by step solution

01

Step 1. Inspecting the y-intercept

Referring to the given graph the type of sinusoid can be determined immediately by inspecting its y- intercept if its at a maximum(highest point) and a minimum(lowest point) or neither

Since the maximum is at its y-intercept, then the graph is a cosine function and hence, A>0.

02

Step 2. Find the amplitude and period

From the graph, ymin=-5ymax=5

A=12(ymax-ymin)A=12(5-(-5))A=12(10)A=5

Using the maximum at x=0, the next maximum occurs at x=8

Therefore,

T=8

03

Step 3. Solve for the equation

ω=2πTω=2π8ω=π4

Therefore, the equation of the graph isy=±5cosπ4x

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