Question

Write a cosine function that has a midline of 5, an amplitude of 2 and a frequency of 3/2

Answer 1

Answer:   y = 2*cos(3pi*x) + 5

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The general template for cosine is

y = A*cos(B(x-C)) + D

where,

|A| = amplitude

B = 2pi/T, with T being the period and T = 1/f, f is the frequency

C = determines horizontal phase shift

D = determines vertical shift, and is midline

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In this case,

midline = 5 means D = 5

amplitude = 2 means A = 2

frequency = 3/2 means the period is T = 2/3, which is the reciprocal of the frequency, so B = 2pi/T = 2pi/(2/3) = 3pi

There is no mention of a phase shift, so C = 0.

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All together we have

A = 2, B = 3pi, C = 0, D = 5

So,

y = A*cos(B(x-C)) + D

y = 2*cos(3pi(x-0)) + 5

y = 2*cos(3pi*x) + 5