# Maths - Trigonometry - Infinite series

## 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.

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