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Calculating values of trig functions

by Felix83
Tags: functions, trig, values
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Felix83
#1
Feb25-05, 10:06 AM
P: 75
How does a calculator approximate a trig function. For example, you punch in sin(37deg) and the calculator will give you 0.6018150232. how does it figure this out?
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CrankFan
#2
Feb25-05, 10:15 AM
P: 135
Read this

or try a web search for "CORDIC."
Moo Of Doom
#3
Feb26-05, 03:08 AM
P: 367
Calculators use partial sums of power series to approximate sine and cosine.

The power series for sine is:

[tex]sin(x) = x - \frac{1}{3!} * x^{3} + \frac{1}{5!} * x^{5} - \frac{1}{7!} * x^{7} + ...[/tex]

Cosine:

[tex]cos(x) = 1 - \frac{1}{2!} * x^{2} + \frac{1}{4!} * x^{4} - \frac{1}{6!} * x^{6} + ...[/tex]

I'm not sure how many terms they usually use, but that doesn't really matter. The more terms, the more accurate.

HallsofIvy
#4
Feb26-05, 09:53 AM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,691
Calculating values of trig functions

Moo Of Doom: I thought for a long time that calculators used power series but I've been told that is not true. Check out CranFan's suggestion about the CORDIC algorithm.
Moo Of Doom
#5
Feb26-05, 12:48 PM
P: 367
Really? Strange... I was just told that... oh well.


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