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# Cosine graph manipulation help.

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)

## Discussions

9 years ago

What you're describing is called a phase shift. Basically, if your original function is

cos(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.

Answer 9 years ago

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)

Answer 9 years ago

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

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.Answer 9 years ago

Thanks that was all I wanted to know.

Answer 9 years ago

After

Answer 9 years ago

Here are some crude ms paint examples:

Answer 9 years ago

Why do you treat the phase shift as a fraction of 2pi? I'm used to it being written cos(wt + d) where w is the angular frequency = 2pi*f.