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Showing content from https://en.cppreference.com/w/cpp/language/../error/error_code/../../numeric/complex/asin.html below:

std::asin(std::complex) - cppreference.com

Computes complex arc sine of a complex value z. Branch cut exists outside the interval [−1, +1] along the real axis.

[edit] Parameters [edit] Return value

If 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 [−π/2, +π/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.

[edit] Notes

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 (-∞,-1) and (1,∞) 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 + √1-z2
).

For any

z

,

\(\small{ \arcsin(z) = \arccos(-z) - \frac{\pi}{2} }\)asin(z) = acos(-z) -

.

[edit] Example

Output:

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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