User talk:PhysOz

Trig Identities (Linear Combinations)
Hi Michael, I am a newbie to editing Wikipedia. I made an edit to Trig Identities which you promptly reverted. I don't know much about editing Wikipedia (for example, I don't know whether this page or the article talk page is the appropriate place for this comment). I erroneously didn't leave a summary of my changes. You have obviously had much experience and made many contributions to wikipedia, but could you please explain your revert? The text talks about a linear combination of any phase-shifted sine wave being a sine wave, but the maths only gives the equation for a pi/2 shifted wave (cosine). My edit generalised the equation for the linear combination of sine waves with arbitrary phase-shifts. I may have made some mistakes with my edit (if so, please correct them or let me know) but I don't understand the need for the revert (see Help:Reverting). Thanks in advance for helping out a newbie. PhysOz 02:48, 1 March 2007 (UTC)


 * The edit appeared hasty and not as clear as what was there, so I may have leapt to the conclusion that you were just experimenting. But let's look at it more closely:


 * $$a\sin x+b\sin(x+y)= \alpha \sin(x+\beta)\,$$


 * where



\alpha = \sqrt{a^2 + b^2 +2ab\cos y}$$,


 * and

\beta = \tan^{-1} \left(\frac{b\sin y}{a + b\cos y}\right) $$.


 * One thing that irritates me is using the Latin letter y for the phase shift on the left and the Greek letter &beta; for the phase shift on the right, and I think notational inconsistency makes me suspicious, and accordingly I didn't look that closely. I now think that it would be a good idea to leave the original as the first example because of the simplicity resulting from orthogonality of sin and cos (in particular, the amplitude is just the square root of the sum of the squares of the separate amplitudes, and everyone's familiar with that pattern from the Pythagorean theorem).  This would occasion some rephrasing of the paragraph before the initial example and then between that and the next one.  (On a less important issue, the final period and the final comma should be inside the math environment; otherwise they get aligned badly on many browsers.) Michael Hardy 03:21, 1 March 2007 (UTC)