#1**+4 **

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)

Alan May 1, 2020

#4**+1 **

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

CPhill May 1, 2020