Calculating values of trig functions

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Calculators approximate trigonometric functions like sine and cosine using algorithms such as CORDIC, rather than solely relying on power series. The CORDIC method efficiently computes these values through iterative calculations, which can be more practical for hardware implementations. While power series expansions provide a theoretical basis for sine and cosine, they may not be the primary method used in modern calculators. The accuracy of the approximation increases with the number of terms used in power series, but CORDIC offers a different approach that balances speed and precision. Overall, understanding these methods enhances comprehension of how calculators deliver trigonometric function values.
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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?
 
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http://math.exeter.edu/rparris/peanut/cordic.pdf

or try a web search for "CORDIC."
 
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Calculators use partial sums of power series to approximate sine and cosine.

The power series for sine is:

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

Cosine:

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

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.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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