Associated Topics || Dr. Math Home || Search Dr. Math

### Derivation of Sum/Difference of Sine, Cosine, Tangent

```
Date: 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

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/
for sine - PDF format)

A very nice exposition of the standard geometric proof is in our
archives:

http://mathforum.org/dr.math/problems/memon12.13.97.html

with a slightly different approach at

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
are Conway's and the complex number method in that last link.

- Doctor Schwa, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Imaginary/Complex Numbers
High School Trigonometry

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search