# Cosine graph manipulation help.

This may not be the best place to ask this question but here we go anyway.

Is there anyway to manipulate a Cosine graph so that the max and min points are the same and the period is the same while the x-intercept is different? (When compared to y = Cos x)

active| newest | oldestcos(2*pi*t)

a phase shift would look something like

cos(2*pi*(t+delta))

wherer delta is the magnitude of the phase shift. Hope this helps.

x-intercept.

For example:

Points before manipulation:

0-pi

Max (0,1)

Min (pi, -1)

Period (2pi)

X-intercept (1/2pi)

After manipulation

0-pi

Max (0,1)

Min (pi,-1)

Period (2pi)

X-intercept (3/4pi)

mightbe able to construct a envelope function which matches your constraints, but that's not a "manipulation," it is a new function, defined either with piecewise segments and continuity conditions, or as an infinite sum of Fourier components.