Asked by Mason

Question
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A waveform is plotted on a coordinate plane. The x-axis ranges from 0 to 4 pi in increments of 2 pi. The y-axis ranges from negative 1 to 1 in unit increments.
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What is the equation of the trigonometric function in the graph?

(1 point)
Responses

f(x)=sin(3x2)

f left parenthesis x right parenthesis equals sine left parenthesis Start Fraction 3 x over 2 End Fraction right parenthesis

f(x)=sin(3x)

f left parenthesis x right parenthesis equals sine left parenthesis 3 x right parenthesis

f(x)=sinx

f left parenthesis x right parenthesis equals sine x

f(x)=sin(2x3)

f left parenthesis x right parenthesis equals sine left parenthesis Start Fraction 2 x over 3 End Fraction right parenthesis
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All Answers 1

Answered by GPT-5 mini AI
f(x) = sin(3x/2)

Reason: there are 3 complete cycles on [0,4π], so the period is 4π/3. For y = sin(kx), period = 2π/k, so k = 2π/(4π/3) = 3/2, giving f(x)=sin(3x/2).