asin¶
- asin(x: array, /) array ¶
Calculates an implementation-dependent approximation of the principal value of the inverse sine for each element
x_i
of the input arrayx
.Each element-wise result is expressed in radians.
Note
The principal value of the arc sine of a complex number \(z\) is
\[\operatorname{asin}(z) = -j\ \ln(zj + \sqrt{1-z^2})\]For any \(z\),
\[\operatorname{asin}(z) = \operatorname{acos}(-z) - \frac{\pi}{2}\]Note
For complex floating-point operands,
asin(conj(x))
must equalconj(asin(x))
.Note
The inverse sine (or arc sine) is a multi-valued function and requires a branch cut on the complex plane. By convention, a branch cut is placed at the line segments \((-\infty, -1)\) and \((1, \infty)\) of the real axis.
Accordingly, for complex arguments, the function returns the inverse sine in the range of a strip unbounded along the imaginary axis and in the interval \([-\pi/2, +\pi/2]\) along the real axis.
Note: branch cuts follow C99 and have provisional status (see Branch Cuts).
- Parameters:
x (array) – input array. Should have a floating-point data type.
- Returns:
out (array) – an array containing the inverse sine of each element in
x
. The returned array must have a floating-point data type determined by Type Promotion Rules.
Notes
Special cases
For real-valued floating-point operands,
If
x_i
isNaN
, the result isNaN
.If
x_i
is greater than1
, the result isNaN
.If
x_i
is less than-1
, the result isNaN
.If
x_i
is+0
, the result is+0
.If
x_i
is-0
, the result is-0
.
For complex floating-point operands, special cases must be handled as if the operation is implemented as
-1j * asinh(x*1j)
.Changed in version 2022.12: Added complex data type support.