I need help with a trig wave formula?

Let P be the period. Then to repeat, this must be divided into 2Pi blocks since cos and sine repeat every 2Pi (360d)

For example if the wave had reached a point at x = (P/2) you would want this to be converted to Pi (half a wave)

So your wave is y = sin(2Pi*(x/p))

Now sin(0) = 0 but cos(0) is 1

So the only difference is that sine starts at amplitude 0 (ie the axis) but cos starts at the peak.

By convention we usually chose sin

Now the max value of sin is +1 And the minimum is –1.

Let your amplitude be A

So the wave is now y= A* sin(2Pi*(x/p))

and the maximum is now y = +A and the minimum is y = –A

Lets say your centre line is 21. So now you need to shift the wave up by 21

Let centre line be at C

So now your equation is y = C + A* sin(2Pi*(x/p))

You do not say where your wave starts, does it start at zero? Or at a peak? or some other place say x'

If it starts at ZERO then your equation is already y = C + A* sin(2Pi*(x/p))

If it starts when say x’ then you have a phase shift to include

Phase shift is just 2pi*(x’/P)

So equation is now

y = C + A* sin(2Pi*(x/p) +2pi*(x’/P) )

same as

y = C + A* sin(2Pi*(x+x’)/P) )

Hi

for some reason it said my name was PAul????

I have re-posted as FOOTMAN!!

Let P be the period. Then to repeat, this must be divided into 2Pi blocks since cos and sine repeat every 2Pi (360d)

For example if the wave had reached a point at x = (P/2) you would want this to be converted to Pi (half a wave)

So your wave is y = sin(2Pi*(x/p))

Now sin(0) = 0 but cos(0) is 1

So the only difference is that sine starts at amplitude 0 (ie the axis) but cos starts at the peak.

By convention we usually chose sin

Now the max value of sin is +1 And the minimum is –1.

Let your amplitude be A

So the wave is now y= A* sin(2Pi*(x/p))

and the maximum is now y = +A and the minimum is y = –A

Lets say your centre line is 21. So now you need to shift the wave up by 21

Let centre line be at C

So now your equation is y = C + A* sin(2Pi*(x/p))

You do not say where your wave starts, does it start at zero? Or at a peak? or some other place say x'

If it starts at ZERO then your equation is already y = C + A* sin(2Pi*(x/p))

If it starts when say x’ then you have a phase shift to include

Phase shift is just 2pi*(x’/P)

So equation is now

y = C + A* sin(2Pi*(x/p) +2pi*(x’/P) )

same as

y = C + A* sin(2Pi*(x+x’)/P) )