Calculating values of trig functions

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Discussion Overview

The discussion revolves around how calculators approximate trigonometric functions, specifically the sine function, when given an angle in degrees. Participants explore different methods and algorithms used in these calculations, including power series and the CORDIC algorithm.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant inquires about the method calculators use to approximate trig functions, specifically mentioning sin(37deg).
  • Another participant suggests looking into the CORDIC algorithm as a potential method used by calculators.
  • A different participant explains that calculators may use partial sums of power series to approximate sine and cosine functions, providing the power series for both functions.
  • One participant expresses uncertainty about the accuracy of the power series method, referencing the CORDIC algorithm as an alternative.
  • A later reply indicates surprise at the suggestion that power series are not used, reflecting the ongoing uncertainty in the discussion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the methods used by calculators, with multiple competing views regarding the use of power series versus the CORDIC algorithm remaining unresolved.

Contextual Notes

There is uncertainty regarding the specific algorithms used in calculators, and the discussion reflects differing opinions on the validity of power series versus CORDIC for approximating trigonometric functions.

Felix83
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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?
 
Mathematics news on Phys.org
http://math.exeter.edu/rparris/peanut/cordic.pdf

or try a web search for "CORDIC."
 
Last edited by a moderator:
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.
 
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.
 
Really? Strange... I was just told that... oh well.
 

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