Difference between revisions of "Trigonometry Functions"
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imported>Dysesothymteric m (→Arctangent: typo) |
imported>Bifmadeinsabbioni |
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== 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. | |||
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 > 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 > 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 | |||