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Chapter 6: Q. 70 (page 411)

Find an equation for each graph.

Short Answer

Expert verified

Equation for the graph is:

y=-cosπx

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=-πymax=π

role="math" localid="1646378197335" A=-12(ymax-ymin)A=-12(π-(-π))A=-12(2π)A=-πA=π

Using the maximum at x=0, the next maximum occurs atx=2π

Therefore,

T=2π

03

Step 3. Solve for the equation

ω=2πTω=2π2πω=1

Therefore, the equation of the graph is

y=-cosπx

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