Subtraction of Trig Functions with a Phase Shift
Date: 09/14/2004 at 14:53:23 From: Jeremy Subject: Subtraction of Trig Functions I am a senior Electrical Engineering student and am currently writing a training manual for my job at an engineering firm. I am now covering 3-phase voltages and have a trig question pertaining to finding the voltage between two phases. My question is this: How do you find the difference between two trigonometric functions with the same frequency, but one is phase shifted by 120 degrees? Here's the explicit problem: cos (wt) - cos (wt - 120), where w = 120*pi. I've tried using Euler's equations, but keep getting stuck.
Date: 09/14/2004 at 15:05:05 From: Doctor Schwa Subject: Re: Subtraction of Trig Functions Hi Jeremy, The technique I learned in trig class for this type of problem, cos (a) - cos(b) is to subtract the identities cos(x+y) = cos x cos y - sin x sin y and cos(x-y) = cos x cos y + sin x sin y to get cos(x+y) - cos(x-y) = -2 sin x sin y. Then from there, you set x + y = a and x - y = b, because you want this formula to match the cos(a) - cos(b) pattern, and after a bit of algebra to solve for x and y, you should get cos a + cos b = -2 sin ((a+b)/2) sin ((a-b)/2). In your case, I guess that turns out to be -2 sin(wt - 60) * sin 60 and it looks to me like that checks out just fine! I'm sure there's a similar pattern using cos + i sin instead of my approach--there always is--but at least on my first attempt, it turned out to be at least as awkward as this one. I hope that helps clear things up! - Doctor Schwa, The Math Forum http://mathforum.org/dr.math/
Date: 09/14/2004 at 18:11:30 From: Jeremy Subject: Thank you (Subtraction of Trig Functions) Dr. Schwa, Thank you so much for your speedy response. It seems a bit late in my college career to become a math guru, but I'm aspiring to become one, on my own, if possible. You're a life saver! Jeremy
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