Talk:Trigonometry Functions

I see no reason for three versions of the Taylor series, and this one is, to me, the most difficult to read. If it has merit, re-add it to the main article, though it must be formatted for being a Stage Function.--DragoonWraith 20:35, 9 May 2006 (EDT)

Taylor Series Variant 3

The idea here is to approximate sin(z) and cos(z) with taylor. Since taylor works best with values close to 0, I think it's a good idea to use sin and cos periodicity as many times as possible. then I used taylor to approximate the functions. (Scripts by bifmadeinsabbioni)

ScriptName Sin(Z)
set Angolo to AngleZ ; Angolo is the angle of which we want to calculate the sin
set Sign to 1 ; it's the sign adjustment of the result 

if (Angolo < 0) ; sin(-z) = -sin(z) 
       set Angolo to Angolo * (-1)
       set Sign to Sign * (-1)
endif

if (Angolo > 180)&& (Angolo <=360) ; if 180<=z<=360 sin(z) = -sin(z-180)
	set Sign to Sign * (-1)
	set Angolo to (Angolo - 180)
endif
 
if (Angolo > 90)&&(Angolo <=180) ; if 90<=z<=180 sin (z) = sin (180-z)
	set Angolo to (180 - angolo)
endif

if (Angolo >45)&&(Angolo <=90) ; if 45<z<90 sin(z) = cos(90-z)
	set Angle to (90 - Angolo)
     	set Angle to (3.14159265 * Angle / 180) ;now in radiants
	set X2 to Angle * Angle
	set X4 to X2 * X2
	set X6 to X4 * X2
	set X8 to X4 * X4
	set SinZ to (1 - X2 / 2 + X4 / 24 - X6 / 720 + X8 / 40320)
	set SinZ to SinZ*Sign
endif

if (Angolo>=0)&&(Angolo<=45)
	set Angle to Angolo
     	set Angle to (3.14159265 * Angle / 180) ;now in radiants
	set X to Angle
	set X3 to X*X*X
	set X5 to X3*X*X
	set X7 to X3*X3*X
	set X9 to X3*X3*X3
	set SinZ to (X - X3 / 6 + X5 / 120 - X7 / 5040 + X9 / 362880)
	set SinZ to SinZ*Sign
endif

ScriptName Cos(Z)
set Angolo to AngleZ ; Angolo is the angle of which we want to calculate the cos
set Sign to 1 ; it's the sign adjustment of the result 
 
if (Angolo < 0) ; cos(-z) = cos(z) 
       set Angolo to Angolo * (-1)
endif

if (Angolo > 180)&& (Angolo <=360) ; if 180<=z<=360 cos(z) = -cos(z-180)
	set Sign to Sign * (-1)
	set Angolo to (Angolo - 180)
endif

if (Angolo > 90)&&(Angolo <=180)   ; if 90<=z<=180 cos (z) = -cos(180-z)
	set Angolo to (180 - Angolo)
	set Sign to Sign * (-1)
endif

if (Angolo >45)&&(Angolo <=90) if 45<z<90 cos(z) = sin(90-z)
	set Angle to (90 - Angolo)
     	set Angle to (3.14159265 * Angle / 180) ;now in radiants
	set X to Angle
	set X3 to X*X*X
	set X5 to X3*X*X
	set X7 to X3*X3*X
	set X9 to X3*X3*X3
	set CosZ to (X - X3 / 6 + X5 / 120 - X7 / 5040 + X9 / 362880)
	set CosZ to CosZ * Sign
endif

if (Angolo>=0)&&(Angolo<=45)
	set Angle to Angolo
     	set Angle to (3.14159265 * Angle / 180) ;now in radiants
	set X2 to Angle * Angle
	set X4 to X2 * X2
	set X6 to X4 * X2
	set X8 to X4 * X4
	set CosZ to (1 - X2 / 2 + X4 / 24 - X6 / 720 + X8 / 40320)
	set CosZ to CosZ * Sign
endif

Arcsine, Arccosine, and Arctangent

Sin=Opp/Hyp - The arcsine is the angle between two points, when the distance is the hypotenuse of the triangle and the opposing side is either the x- or the y-difference (whatever is shorter). To get the z-angle (left/right) between two objects in Oblivion you can use the function GetHeadingAngle. But when you need the x-angle (up/down) you still have to calculate the arcsin.