Derivation of Sum/Difference of Sine, Cosine, TangentDate: 02/16/2002 at 22:32:24 From: Meredith Subject: Derivation of the Sum/Difference of Sine, Cosine, and Tangent How can I find the derivation of the sum/difference of sine, cosine, and tangent? Date: 02/17/2002 at 00:07:41 From: Doctor Schwa Subject: Re: Derivation of the Sum/Difference of Sine, Cosine, and Tangent Hi Meredith, A beautiful geometric approach is at Geometry of Addition and Subtraction Formulas - Smiley http://www.math.uaa.alaska.edu/~smiley/trigproofs.html and another approach, which I got from John Conway, is at Trig/Analyt Handouts - Joshua Zucker http://www.castilleja.org/faculty/josh_zucker/gunn/trig/handouts/ (select the link to "a derivation of the angle addition formula for sine - PDF format) A very nice exposition of the standard geometric proof is in our archives: Cosine Addition Formula http://mathforum.org/dr.math/problems/memon12.13.97.html with a slightly different approach at Sine and Cosine Addition Formulas http://mathforum.org/dr.math/problems/phara.11.29.00.html There's also the derivation using complex numbers, which is suggested at Trigonometric Functions and Euler's Identity http://mathforum.org/dr.math/problems/jungbok4.10.98.html and made much more explicit at Euler's Formula http://mathforum.org/dr.math/problems/wolf1.27.98.html I hope at least one of those methods appeals to you. Let me know if you would like more information about any of them. My favorites are Conway's and the complex number method in that last link. - Doctor Schwa, The Math Forum http://mathforum.org/dr.math/ |
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