How does the calculator calculate the values of trigonometric functions?

The [b]CORDIC algorithm[/b] (short for [i]Coordinate Rotation Digital Computer[/i]) is a clever method used by computers to calculate trigonometric functions such as sine and cosine, while using very few [b]expensive multiplications[/b].[br][br]CORDIC works by rotating a point in [b]cleverly chosen[/b], progressively smaller steps. This approach replaces most multiplications with [b]bit shifting[/b] (dividing by powers of 2 in binary), which is very fast and simple for computers. By performing many [b]small rotations[/b] and combining their effects, the algorithm [b]gradually produces [/b]a close enough approximation.[br][br]Because it is efficient, CORDIC is widely used in calculators, computer graphics, robotics, and signal processing, especially in devices that do not have powerful hardware.[br][br]More information:[br]https://en.wikipedia.org/wiki/CORDIC

Here is the derivation of the matrix transformation:[br](expressing the trigonometric functions in terms of powers of 2 and square roots)