A very good approximation is given by this polynomial.
arcsin(x) = pi/2 - sqrt(1 - x)(a0 + a1*x + a2*x^2 + a3*x^3)
where constant are as follow:
a0 = 1.5707288
a1 = -0.2121144
a2 = 0.0742610
a3 = -0.0187293
Tray it and see if this polynomial will solve your problem.
Al.




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