Trig Functions Maclaurin Series

trigonometry-functions-maclaurin.js

/*
	These are unoptimized recreations of the built-in trigonometric
	functions as defined by Maclaurin / Taylor series.
*/

function factorial( number ) {
	
	var product = Math.max(1,number)
	
	while( number-- > 1 ) {
		product *= number
	}
	
	return product
}

function sin( x, iterations ) {
	
	var sum = 0
	
	for( var n=0; n < iterations; n++ ) {
		var numerator = Math.pow(-1, n) * Math.pow(x, 2 * n + 1 )
		var denominator = factorial( 2 * n + 1 )
		sum += numerator / denominator
	}
	
	return sum
}

function cos( x, iterations ) {
	
	var sum = 0
	
	for( var n=0; n < iterations; n++ ) {
		var numerator = Math.pow(-1, n) * Math.pow(x, 2 * n)
		var denominator = factorial( 2 * n )
		sum += numerator / denominator
	}
	
	return sum
}

function tan( x, iterations ) {
	return sin( x, iterations ) / cos( x, iterations )
}

function sec( x, iterations ) {
	return 1 / cos( x, iterations )
}

function cot( x, iterations ) {
	return cos( x, iterations ) / sin( x, iterations )
}

function csc( x, iterations ) {
	return 1 / sin( x, iterations )
}

function eRaisedTo( x, iterations ) {
	
	var sum = 1
	
	for( var n=1; n < iterations; n++ ) {
		sum += Math.pow(x, n) / factorial( n )
	}
	
	return sum
}