Question

Question
Use the image to answer the question.

A waveform graph is shown on a coordinate plane. The x axis is labeled in increments of start fraction pi over 6 end fraction, going from 0 to start fraction 2 pi over 3 end fraction. The y axis is labeled in increments of 2, going from negative 2 to 2.
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Based on the set of points in the graph, determine the equation that would match the graph.

(1 point)
Responses

f(θ)=1.5cos(π3θ)

f of theta is equal to 1 point 5 cosine open paren pi over 3 theta close paren

f(θ)=1.5sin(π3θ)

f of theta is equal to 1 point 5 sine open paren pi over 3 theta close paren

f(θ)=1.5cos(3θ)

f of theta is equal to 1 point 5 cosine 3 theta

f(θ)=1.5sin(3θ)

f of theta is equal to 1 point 5 sine 3 theta
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Answer 1

f(θ) = 1.5 cos(3θ)

Reason: amplitude = 1.5. The graph completes one full cycle from 0 to 2π/3, so period = 2π/3 ⇒ b = 2π/(2π/3) = 3. At θ = 0 the graph is at a maximum (1.5), so use cosine.