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ArcSin

 ArcSin[z]gives the arc sine of the complex number .
• Mathematical function, suitable for both symbolic and numerical manipulation.
• All results are given in radians.
• For real between and , the results are always in the range to .
• For certain special arguments, ArcSin automatically evaluates to exact values.
• ArcSin can be evaluated to arbitrary numerical precision.
• ArcSin automatically threads over lists.
• ArcSin[z] has branch cut discontinuities in the complex plane running from to and to .
 Scope   (7)
Evaluate numerically:
Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
The precision of the output can be much lower than the precision of the input:
Simple exact values are generated automatically:
Parity transformation is automatically applied:
ArcSin threads element-wise over lists and matrices:
ArcSin can deal with real-valued intervals from :
Infinite arguments give symbolic results:
ArcSin can be applied to power series:
Find series expansions at branch points and branch cuts:
ArcSin threads over explicit lists as well as over sparse arrays:
 Applications   (4)
Plot the real and imaginary parts of ArcSin:
Plot the Riemann surface of ArcSin:
Find the angle between two 3D vectors:
Modeling Levy's second arc sine law:
Compose with the inverse function:
Use PowerExpand to disregard multivaluedness of the ArcSin:
Use TrigToExp to express through logarithms and square roots:
This shows the branch cuts of the ArcSin function:
Expand assuming real variables:
Solve an inverse trigonometric equation:
Solve for zeros:
Integrals:
Laplace transforms:
ArcSin is a special case of various mathematical functions:
Generically :
On branch cuts machine-precision inputs can give numerically wrong answers:
In traditional form parentheses are needed around the argument:
Nested integrals:
Calculate numerical values by iteration:
Plot ArcSin at integer points:
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