How does a calculator calculate the Trig functions?
What algorythm do they use?
2006-11-10 03:04:23 · 6 answers · asked by theFo0t 3 in Science & Mathematics ➔ Mathematics
Trig functions can be calculated using the first several terms of a suitable series. However, faster algorithms have been designed to maximize speed. See the source for details of HP calculators. To quote:
"Cordic is the name of the secret of the fast hardware-algorithm use[d] by all hand held calculators starting with HP35, to compute log, sine and others."
It first calculates tan then uses it for sin and cos, example:
sin x = tan x / √( 1 + tan²x )
Only addition, subtraction and shifting are used.
2006-11-10 04:25:38 · answer #1 · answered by p_ne_np 3 · 0⤊ 0⤋
well, the 6 trig values for any angle that is a multiple of 3 there's a "nice" algebraic number for it. but 23 isn't a multiple of three, so you'll have to extrapolate by finding the two closest values (ex. sin 21 and sin 24) and averaging them out.
2016-05-22 02:47:57 · answer #2 · answered by Anonymous · 0⤊ 0⤋
The formulas for the expansion series for each function are hard wired in the chips. The number of actual calculations made just to get a sin or cos is pretty astounding
http://mathworld.wolfram.com/SeriesExpansion.html
2006-11-10 03:09:44 · answer #3 · answered by SteveA8 6 · 1⤊ 0⤋
Probably uses a power series.
cos(x) = 1-x^2/2!+x^4/4!-x^6/6!+....
sin(x) = x-x^3/3!+x^5/5!+....
f(x) = f(0)+f'(0)x+f''(0)x^2/2!+f'''(0)x^3/3!+...
2006-11-10 03:15:32 · answer #4 · answered by Anonymous · 0⤊ 0⤋
every symbol is wrote on the calculator
sin is sin
but if u had a question like this
sin A =0.1257
so measure angle A is by that way : press shift sin 0.1257
2006-11-10 03:13:08 · answer #5 · answered by nano_1992_fun 2 · 0⤊ 1⤋
they are the sums of infinite series ....they just don't use the entire series due to the lack of infinite decimal places.
2006-11-10 03:17:09 · answer #6 · answered by Brian D 5 · 0⤊ 0⤋