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Chapter 6: Q. 66 (page 410)

Find an equation for each graph.

Short Answer

Expert verified

Equation for the graph is:

y=-2sinπ2x

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

At its y-intercept neither maximum or nor minimum, then the graph is a sine function and hence, A<0.

02

Step 2. Find the amplitude and period

From the graph, ymin=-2ymax=2

A=12(ymax-ymin)A=12(2-(-2))A=12(4)A=2

Using the maximum at x=1, the next maximum occurs atx=4

Therefore,

T=4

03

Step 3. Solve for the equation

ω=2πTω=2π4ω=π2

Therefore, the equation of the graph is

y=-2sinπ2x

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