Convert waveform formula to 'usual' cos sin formula to sketch graph

[Ian Wright]

Hi.
I am used to drawing cos sin waves graphs from formulas that look like:

Y = A cos (B (x-c) ) + D
where A = amplitude, B = Period (2pie / B), C= Horizontal Phase Shift, D=Vertical Shift.

But I have the formula Vt = 10cos (650t + 0.0015) and cannot understand how it relates to the formula's I am used to? Does anyone have any ideas of where I get the period and phase shifts from it?
Many Thanks

 

[Harald Kapp]

I am used to drawing cos sin waves graphs from formulas that look like:

Maybe look like but are the same as. Have a closer look at this equation:

Y = A cos (B (x-c) ) + D

This should be
Y = A cos (B*x-c) ) + D as the phase shift c is fixed and not time variable. The time variable part would be the frequency (or equivalent to the inverse of the period).
Then the correspondence is obvious.

B = Period (2pie / B)

This makes no sense as B = 2*Pi/B means B is fixed at B = sqrt(2*Pi). The period of a sine is defined as 1/f where f is the frequency in Hz.

 

[dorke]

This may help you (from wiki):



There is no "D=Vertical Shift" here,but it can be easily added if needed.
We call it the "DC part", i.e zero frequency part.

 

[Ratch]

Hi.
I am used to drawing cos sin waves graphs from formulas that look like:

Y = A cos (B (x-c) ) + D
where A = amplitude, B = Period (2pie / B), C= Horizontal Phase Shift, D=Vertical Shift.

But I have the formula Vt = 10cos (650t + 0.0015) and cannot understand how it relates to the formula's I am used to? Does anyone have any ideas of where I get the period and phase shifts from it?
Many Thanks

I don't see what the problem is. Simply convert the coefficient 650 into a frequency as shown below.

Below is plot of the original equation.

And, it matches with the revised equation.

Ask if you have any questions.

Ratch

 

[Harald Kapp]

I don't see what the problem is.

Have a close look at the way the parentheses are set. The equation as posted by the op makes not much sense.

 

[Ratch]

Have a close look at the way the parentheses are set. The equation as posted by the op makes not much sense.

True, it is a clunky, clumsy way to present a simple trig equation. But, I was trying to show him how to find the frequency and period of the second equation involving the 650 times "t" term. I let him figure out how to simplify the phase change term of 10.

Ratch

 

[Ian Wright]

thanks so much guys, think I've got it now. Much appreciated.