# Complex Computations, Inverse Trigonometric Functions

Arcsine: ASin(x) = {ASin(v), Ln(u + SqRt(u^2 − 1))}
where u = a + b and v = a − b
and a = SqRt((x.r+1)^2 + x.i^2)/2 and b = SqRt((x.r−1)^2 + x.i^2)/2.
See: Inverse Sine -- From MathWorld
and Wolfram Function Evaluation

Arccosine: ACos(x) = {ACos(v), −Ln(u + SqRt(u^2 − 1))}
where u = a + b and v = a − b
and a = SqRt((x.r+1)^2 + x.i^2)/2 and b = SqRt((x.r−1)^2 + x.i^2)/2.
See: Inverse Cosine -- From MathWorld
and Wolfram Function Evaluation

Arctangent: ATan(x) = {ATan(2*x.r/d1)/2, Ln((x.r^2 + (x.i + 1)^2)/d2)/4}
where d1 = 1 − x.r^2 − x.i^2, d2 = x.r^2 + (x.i − 1)^2
and x is not equal to i or −i.
See: Inverse Tangent -- From MathWorld
and Wolfram Function Evaluation

Arctangent2: ATan2(y, x) = −i*Ln((x + i*y)/SqRt(x^2 + y^2))
where the natural log of a complex number is used and y/x is not equal to i or −i.
See: Inverse Tangent -- From MathWorld
and Wolfram Function Definition

Arccotangent: ACot(x) = ATan(1/x),
but if x = 0, ACot(0) = +/−Pi/2, +Pi/2 is principal value,
and x is not equal to i or −i.
See: Inverse Cotangent -- From MathWorld
and Wolfram Function Evaluation

Arcsecant: ASec(x) = ACos(1/x),
but ASec(0) is not defined.
See: Inverse Secant -- From MathWorld
and Wolfram Function Evaluation

Arccosecant: ACsc(x) = ASin(1/x),
but ACsc(0) is not defined.
See: Inverse Cosecant -- From MathWorld
and Wolfram Function Evaluation