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) + ( 2a5 / 15) + ...
inverse functions
sin-1(x) = x + ( x3 / 3!) + ( 9x5 / 5!) + (225 x7
/ 7!) + ...
cos-1(x) = PI/2 - x - ( x3 / 3!) - (9 x5 / 5!) - ( 225 x7 / 7!) + ...
tan-1(x) = x - ( x3 / 3) + ( x5 / 5) - ( x7 / 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.
