# Cosine graph manipulation help. Answered

I am starting a electric vehicle project and have a math question which is relevant.
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)

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## Discussions

I am looking for a manipulation in which both the max and min points stay in the same place as well as having the same period but one that changes the
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)

You can't, not if you wan't a simple sinusoid. Your constraints are inconsistent, as you should be able to see. You might be 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.