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# What is the equation of the cosine function shown?

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What is the equation of the cosine function shown? May 1, 2020

#1
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The midline is at y = 2, so the amplitude, A = 10 - 2 = 8.  The period, T = 6pi - 2pi = 4pi.

The form of the equation will be y = 2 - A*cos(2*pi*x/T)

May 1, 2020
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Can you simplify that a bit please? I'm trying to write it in the form of the function/equation if possible.

Guest May 1, 2020
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I'm sure you can replace A by 8 and T by 4pi !!

Alan  May 1, 2020
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We have this form :

y  =  Acos [ B (x + C) ] + D

A = the amplitude  =  [ 10 - -6] / 2  = 8

B  = the  number of periods in 2pi   =  2pi / the period

The period  = 4 pi   ....so...

B =  2pi / [ 4pi]   =  1/2

C  = the phase shift

The normal cosine curve  has its first max at x = 0

This one has its first max at 2pi

So.....this is a shift to the right of 2pi

So...   C   =  -2pi

D = the midline  =   [ 10 - 6] / 2   =  4/2  = 2

So....the function is

y = 8cos [ (1/2) (x - 2pi) ] + 2

See the graph here : https://www.desmos.com/calculator/bztp33f42u   May 1, 2020