// These basic sine and cosine threads are used mainly for the bangalore bomb explosions. Usually, the bangalores are placed with 90,180,270,360 yaw-angles.
// The explosion emitter lies 100 units away from the bangalore's origin. If the bangalore's angle is at a weird angle like 55,137,253,351 degrees,
// then sine & cosine threads help to calculate the x-axis & y-axis coords for the explosion emitter. The 100 units value is the hypotenuse distance from the bangalore's origin.
// Below shows the old code example, and 2 modified code examples using sine & cosine threads.
//
// 	local.bangaloreold.origin = ( 100 200 -50 )
// 	local.bangaloreold.angles = ( 0 -90 0 )
// 	local.explosionold.origin = local.bangalore1.origin + ( 0 -100 0 )
//
// 	local.bangalore2.origin = ( 100 200 -50 )
// 	local.bangalore2.angles = ( 0 55 0 )
// 	local.sin2 = (waitthread global/math.scr::sine 55) * 100	// y-axis
// 	local.cos2 = (waitthread global/math.scr::cosine 55) * 100 	// x-axis
// 	local.explosion2.origin = local.bangalore2.origin + ( local.cos2 local.sin2 0 )
//
// 	local.bangalore3.origin = ( 100 200 -50 )
// 	local.bangalore3.angles = ( 0 55 0 )
// 	local.sin3 = (waitthread global/math.scr::sine local.bangalore3.angles[1]) * 100
// 	local.cos3 = (waitthread global/math.scr::cosine local.bangalore3.angles[1]) * 100
// 	local.explosion3.origin = local.bangalore3.origin + ( local.cos3 local.sin3 0 )
//
// To verify the sine and cosine values, simply add the code lines below after waitthread maps/global/math.scr::
// 	iprintlnbold("local.sin2 = " + local.sin2)
// 	iprintlnbold("local.cos2 = " + local.cos2)

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// Maclaurin series expansion equations are used for "sin(degrees) = Y coordinate" and "cos(degrees) = X coordinate".
// 1/(2!) = 0.5, 1/3! = 0.16666666666, 1/4! = 0.04166666666, 1/5! = 0.00833333333, 1/6! = 0.00138888888, 
// 1/7! = 0.00019841269, 1/8! = 0.00002480158, 1/9! = 0.00000275573, 1/10! = 0.00000027557, 1/11! = 0.00000002505
// This script only goes up to 11!. For more accuracy, add more factorials to the sine/cosine threads below & add more decimal places to all values, including PI.

// sin(n) = n - n^3/3! + n^5/5! - n^7/7! + n^9/9! - n^11/11! + n^13/13! - n^15/15! + n^17/17! ..., "n" radians

sine local.degrees: 

	local.PI = 3.14159265359 // MOHAA console may only display first 3 decimals (3.142), but the game does compute beyond 3 decimals.
	if(local.degrees >= 180) { local.degrees = local.degrees - 360 } // local.player.angles[1] = local.degrees can sometimes be > 180 and < 360.
									 // for sin/cos to work, degrees must be between -180, 0, 180.
	local.radians = local.degrees * (local.PI / 180)

	local.rad3rd = local.radians * local.radians * local.radians // = n^3
	local.rad5th = local.radians * local.radians * local.radians * local.radians * local.radians // = n^5
	local.rad7th = local.radians * local.radians * local.radians * local.radians * local.radians * local.radians * local.radians // = n^7
	local.rad9th = local.radians * local.radians * local.radians * local.radians * local.radians * local.radians * local.radians * local.radians * local.radians // = n^9
	local.rad11th = local.radians * local.radians * local.radians * local.radians * local.radians * local.radians * local.radians * local.radians * local.radians * local.radians * local.radians // = n^11

	local.sine = local.radians - (local.rad3rd * 0.16666666666) + (local.rad5th * 0.00833333333) - (local.rad7th * 0.00019841269) + (local.rad9th * 0.00000275573) - (local.rad11th * 0.00000002505)
end local.sine

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// cos(n) = 1 - n^2/2! + n^4/4! - n^6/6! + n^8/8! - n^10/10! + n^12/12! - n^14/14! + n^16/16! ..., "n" radians

cosine local.degrees: 

	local.PI = 3.14159265359
	if(local.degrees >= 180) { local.degrees = local.degrees - 360 }

	local.radians = local.degrees * (local.PI / 180)

	local.rad2nd = local.radians * local.radians // = n^2
	local.rad4th = local.radians * local.radians * local.radians * local.radians // = n^4
	local.rad6th = local.radians * local.radians * local.radians * local.radians * local.radians * local.radians // = n^6
	local.rad8th = local.radians * local.radians * local.radians * local.radians * local.radians * local.radians * local.radians * local.radians // = n^8
	local.rad10th = local.radians * local.radians * local.radians * local.radians * local.radians * local.radians * local.radians * local.radians * local.radians * local.radians // = n^10

	local.cosine = 1 - (local.rad2nd * 0.5) + (local.rad4th * 0.04166666666) - (local.rad6th * 0.00138888888) + (local.rad8th * 0.00002480158) - (local.rad10th * 0.00000027557)
end local.cosine



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// Not needed for sine & cosine threads, but can be used to verify math. When player faces 45, 135, 225, 315 degrees, tangent should = 1 or -1. 
//
//	local.sin = waitthread global/math.scr::sine 45 // 45 degrees
//	local.cos = waitthread global/math.scr::cosine 45
//	
// 	local.mathtest = waitthread global/math.scr::tangent local.sin local.cos
//	iprintlnbold("sin(45 degrees) = " + local.sin + " ... cos(45 degrees) = " + local.cos)
//	iprintlnbold("tan(45 degrees) = " + local.mathtest)
//
// tan(n) = sin(n) / cos(n)

tangent local.sine local.cosine:

	local.tangent = local.sine / local.cosine
end local.tangent

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// Not needed for sine & cosine threads, but can be used to verify math. Example: if horizontaldist = 100, then hypotenusedist should = 99 or 100 every time.
// The hypotenusedist will mostly deviate from 100 as the player faces +/- 180 degrees or +/- 3.142 radians. 
//
//	local.mathtest = waitthread global/math.scr::pythagorean local.sin local.cos 100
//	iprintlnbold("distance of 100; hypotenusedist = " + local.mathtest)
//
// hypotenuse^2 = length^2 + width^2 ... p^2 = x^2 + y^2.

pythagorean local.sine local.cosine local.distance:

	local.hypotenusedist = ((local.sine * local.sine) + (local.cosine * local.cosine)) / local.distance
end local.hypotenusedist

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// Not needed for sine & cosine threads, but can be used to verify math:
//
// 	local.mathtest = waitthread global/math.scr::factorial 7
//	iprintlnbold("7! = " + local.mathtest)
//
// n! = n * (n-1) * (n-2) * (n-3) * (n-4) * (n - (n-1)); and (n - (n-1)) = 1; // 0!=1, 1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720, 7!=5040, 8!=40320

factorial local.n:

	local.factorial = 1

	for(local.p = 0; local.p < local.n; local.p++)
	{
		local.factorial = local.factorial * (local.n - local.p)
	}
end local.factorial