Exact Sin Calculus: Solving for Trigon Funcs Without Triangles

[vjacheslav]

Hi!
While computer programming Us encountered problem of exact calculus of trigonometry funcs.
As is well known, all calculators and comp progs do x for Sin
and x^2/2 for Cos on 0..Pi/2 and so on. It seems insufficient.
While solving - next problem:
trigon func definition without triangle.

 

[SteamKing]

Hi!
While computer programming Us encountered problem of exact calculus of trigonometry funcs.
As is well known, all calculators and comp progs do x for Sin
and x^2/2 for Cos on 0..Pi/2 and so on. It seems insufficient.
While solving - next problem:
trigon func definition without triangle.

I'm sorry, but this doesn't make a lot of sense. Can you explain it better?

 

[bhillyard]

I think you may be thinking of how a calculator/computer generates the sin/cosine of a number.
They will use several terms to calculate the value.
I don't think it will be the first few terms of a Taylor series for the function - the convergence is likely to be too slow. The only case I recall is the sine function in the Fortran library for a Univac 1108. This used a fifth degree expression in x² - I don't remember the coefficients.

 

[SteamKing]

This article describes one basic algorithm which can be used to calculate trigonometric and hyperbolic functions on relatively primitive computers:

http://en.wikipedia.org/wiki/CORDIC

Many of the processors nowadays have microcode for calculating trig functions built into the CPU itself.