Project64 Forums Blog Space :D Sine of One Degree
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#1
30th June 2011, 11:20 PM
 HatCat Alpha Tester Project Supporter Senior Member Join Date: Feb 2007 Location: In my hat. Posts: 16,236
Blog Space :D Sine of One Degree

Storing further text notes on my Flash drive just doesn't render my notes out in the eminent way I may very well need, so I'm just going to take notes via spam on a vBulletin board.

So method here is that I've based off the original expression for the sine of one degree:

Which this web page explains how to derive using basic trigonometric properties,
http://www.efnet-math.org/Meta/sine1.htm

Now that expression looks huge as Hell, but the only two problems I can see are that a) its definition is in terms of the imaginary unit i = sqrt(-1) and that b) tediousness in writing, in spite of the fact that two very large components of that expression are repeatedly used throughout the expression and can be replaced.

After hours of working with imaginary or complex numbers, I've [possibly mistakenly] simplified that expression down to:
[(a + b)^2 - 64] / 512(a + b)

Where a is that frequently used component, stemming from [4 * sqrt(2)] to [4 * sqrt(5) * sqrt(25 + 11(sqrt5))], and b is 16i * sqrt(8 + ... - 2 * sqrt(2) * sqrt(25 + 11 * sqrt(5)).

I've been working several days now on simplifying both expressions (mostly analytic factorization) to a clearer real-number solution for the exact value of the sine of one degree.