Question

The waveform extends infinitely in both left and right directions. Starting in the third quadrant it goes through left parenthesis 0 comma 0 right parenthesis, and passes through y equals zero again at 3 pi on the x-axis. It reaches alternate positive and negative peaks of y equals 1 and y equals negative 1 respectively. The waveform completed two positive and one negative peak from 0 to 4 pi approximately on the x-axis.

What is the equation of the trigonometric function in the graph?

(1 point)
Responses

f(x)=sin(2x3)

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

f(x)=sinx

f left parenthesis x right parenthesis equals sine x

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)

Answer 1

f(x) = sin(2x/3)

Reason: B = 2/3 gives period P = 2π/(2/3) = 3π, so zeros occur at 0 and 3π and there is one full cycle plus a third of another from 0 to 4π, producing two positive peaks and one negative peak. Also sin(2x/3) crosses 0 at x=0 from negative to positive, matching the described start in the third quadrant.