Computes complex arc sine of a complex value z. Branch cut exists outside the interval [â1, +1] along the real axis.
[edit] Parameters [edit] Return valueIf no errors occur, complex arc sine of z is returned, in the range of a strip unbounded along the imaginary axis and in the interval [âÏ/2, +Ï/2] along the real axis.
Errors and special cases are handled as if the operation is implemented by -i * std::asinh(i * z), where i is the imaginary unit.
Inverse sine (or arc sine) is a multivalued function and requires a branch cut on the complex plane. The branch cut is conventionally placed at the line segments (-â,-1) and (1,â) of the real axis.
The mathematical definition of the principal value of arc sine is \(\small \arcsin z = -{\rm i}\ln({\rm i}z+\sqrt{1-z^2})\)arcsin z = -iln(iz + â1-z2
).
For any
z,
\(\small{ \arcsin(z) = \arccos(-z) - \frac{\pi}{2} }\)asin(z) = acos(-z) -.
[edit] ExampleOutput:
asin(-2.000000,0.000000) = (-1.570796,1.316958) asin(-2.000000,-0.000000) (the other side of the cut) = (-1.570796,-1.316958) sin(acos(-2.000000,-0.000000) - pi / 2) = (2.000000,0.000000)[edit] See also
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