How do calculators calculate sin, cos, tan and square root?

Question

please don't say unit circle, thats how primitive humans calculate it.

i know theres some function of radians that gives sin and cos (and hence tan).

i have a deep understanding of computers, down to the semiconductor, i know C and C++, and i have a great understanding of geometry and trigonometry.

Please dont simplify anything, and no stupid answers!

Answer 1

Most calculators find trig functions using the Taylor series.

Answer 2

Some calculators, when series or natural logarithms would be too slow, use newton's method for roots, that is

to find the root of a number n, using the estimate x, we would take the previous estimate plus n over the previous estimate, and divide that by two

For example, the square root of 19, using 1 as our first estimate,

1

1+19/1=20/2=10

10+19/10=11.9/2=5.95

etc until the answer is accurate to eight digits

As far as sine goes, while I'm not sure how calculators do it, if you're looking for something you COULD do with a calculator, you can always use the definition of sin, which is an infinite sum, and just iterate n until, again, the answer is accurate to eight decimal places (in other words, the first eight decimal places don't change between iterations). That definition can be found in the second link I provided.