C12 = 0.7853134
C32 = -0.3216147
C52 = 0.0363551
// Apollo’s approx for sin(π/2 y)/2
f = y => {
const y2 = y * y;
return ((C52 * y2 + C32) * y2 + C12) * y;
}
// Taylor series
taylor = y => {
const y2 = y * y;
return ((0.0398463 * y2 - 0.3229820) * y2 + 0.7853981) * y;
}
errorA = y => Math.sin(halfPi * y) / 2 - f(y)
errorT = y => Math.sin(halfPi * y) / 2 - taylor(y)
halfPi = Math.PI / 2
N = 120
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