Re: One small math remark... Message #7 Posted by Vieira, Luiz C. (Brazil) on 13 May 2003, 12:34 p.m., in response to message #4 by glynn
Hi;
after Taylor's polynomial development, we have:
sin(X) = (X1)/1! - (X3)/3! + (X5)/5! - (X7)/7! + .... and:
cos(X) = -(X2)/2! + (X4)/4! - (X6)/6! + (X8)/8! + ....
Each new term is a lot smaller than the previous one, and in the calculator's predefined accuracy, when a new term no longer changes the final result, the other ones will not change too, so it's time to stop. The relation between sine and cosine is known as:
(sin(X))2 + (cos(X))2 = 1 (Pythagorean)
Also, the tangent relation is:
sin(X)/cos(X) = tan(X)
The key is finding either sin(X) or cos(X) and apply final two identities to compute tan(X) and the remaining cos(X) if sin(X) is found or vice-versa.
Please, if I miss(pelled) something or committed a math crime in here, I plied guilty and ask for mercy... I beg to the jury to consider that I wrote it by heart, do not have my notes or books in hands.
Otherwise, is that easy to get?
My US$ 0.02 contribution.
Luiz C. Vieira - Brazil
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