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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The graph passes through the following points: left parenthesis 0 comma 1.5 right parenthesis, left parenthesis start fraction pi over 6 end fraction comma 0 right parenthesis, left parenthesis start fraction pi over 3 end fraction comma negative 1.5 right parenthesis, left parenthesis start fraction pi over 2 end fraction comma 0 right parenthesis, left parenthesis start fraction 2 pi over 3 end fraction comma 1.5 right parenthesis.

Based on the set of points in the graph, determine the equation that would match the graph.

(1 point)
Responses

f(θ)=1.5sin(3θ)

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

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)

Answer 1

f(θ) = 1.5 cos(3θ)

Reason: f(0)=1.5 so it must be a cosine. The first zero at θ = π/6 gives k from cos(kθ)=0 when kθ = π/2 ⇒ k = (π/2)/(π/6) = 3. This also matches the other points.