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

Discussion in 'Electronics Homework Help' started by Ian Wright, Nov 21, 2017.

1. Ian Wright

6
0
Nov 21, 2017
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

2. Harald KappModeratorModerator

10,806
2,437
Nov 17, 2011
Maybe look like but are the same as. Have a closer look at this equation:

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.

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.

3. dorke

2,342
665
Jun 20, 2015

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.

4. Ratch

1,088
331
Mar 10, 2013
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

5. Harald KappModeratorModerator

10,806
2,437
Nov 17, 2011
Have a close look at the way the parentheses are set. The equation as posted by the op makes not much sense.

6. Ratch

1,088
331
Mar 10, 2013
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

7. Ian Wright

6
0
Nov 21, 2017
thanks so much guys, think I've got it now. Much appreciated.