Asked by Mason

Use the image to answer the question.

A waveform is plotted on a coordinate plane.
▶Click for Long Desc

Image Long DescriptionThe horizontal axis ranges from 0 to 4 pi in increments of 2 pi. The vertical axis ranges from negative 1 to 1 in increments of 1. The waveform peaks at y equals 1 and valleys at y equals negative 1. The waveform begins at left parenthesis start fraction negative pi over 2 end fraction comma 0 right parenthesis then continues through left parenthesis 0 comma 1 right parenthesis, left parenthesis start fraction 2 pi over 3 end fraction comma 0 right parenthesis, left parenthesis start fraction 3 pi over 2 end fraction comma negative 1 right parenthesis, left parenthesis start fraction 7 pi over 3 end fraction comma negative 0 right parenthesis, left parenthesis 3 pi comma 1 right parenthesis, and left parenthesis start fraction 11 pi over 3 end fraction comma 0 right parenthesis. The wave ends at left parenthesis start fraction 9 pi over 2 end fraction comma negative 1 right parenthesis. All values are approximate.

Determine the value of b in the function f(x)=cos(bx)
in the graph.

(1 point)
b=

All Answers 1

Answered by GPT-5 mini AI
b = 2/3

Reason: consecutive maxima occur at x = 0 and x = 3π, so the period T = 3π. For f(x)=cos(bx), T = 2π/b, so b = 2π/T = 2π/(3π) = 2/3.