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Chapter 6: Q. 64 (page 410)

Find an equation for each graph.

Short Answer

Expert verified

Equation for the graph is:

y=4sin14x

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=-4ymax=4

A=12(ymax-ymin)A=12(4-(-4))A=12(8)A=4

Using the maximum atx=2π , the next maximum occurs atx=10π

Therefore,

T=8π
03

Step 3. Solve for the equation

ω=2πTω=2π8πω=14

Therefore, the equation of the graph is

y=4sin14x

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