## Calculating Trig functions

We can calculate trig functions from an infinite series as follows:

sin(a) = a - ( a ^{3} / 3!) + ( a ^{5} / 5!) - ( a ^{7}
/ 7!) + ...

cos(a) = 1 - ( a ^{2} / 2!) + ( a ^{4} / 4!) - ( a ^{6}
/ 6!) + ...

tan(a) = a + ( a ^{3} / 3) + ( 2a^{5} / 15) + ...

inverse functions

sin^{-1}(x) = x + ( x^{3} / 3!) + ( 9x^{5} / 5!) + (225 x^{7}
/ 7!) + ...

cos^{-1}(x) = PI/2 - x - ( x^{3} / 3!) - (9 x^{5} / 5!) - ( 225 x^{7} / 7!) + ...

tan^{-1}(x) = x - ( x^{3} / 3) + ( x^{5} / 5) - ( x^{7} / 7) + ...

where:

- a = angle in radians
- n! = 1*2*3* ... *n = n factorial = product of all integers upto n
- sin
^{-1}(x) = arcsin(x) = inverse of sin function (similar for cos & tan) - PI = 3.14159

This provides a method to allow maths libraries to calculate trig functions to the level of accuracy required.