ArcSin

ArcSin[z]
gives the arc sine of the complex number .

DetailsDetails

  • 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 .

Background
Background

  • ArcSin is the inverse sine function. For a real number , ArcSin[x] represents the radian angle measure such that .
  • ArcSin automatically threads over lists. For certain special arguments, ArcSin automatically evaluates to exact values. When given exact numeric expressions as arguments, ArcSin may be evaulated to arbitrary numeric precision. Operations useful for manipulation of symbolic expressions involving ArcSin include FunctionExpand, TrigToExp, TrigExpand, Simplify, and FullSimplify.
  • ArcSin is defined for complex argument via sin^(-1)(z)=-ⅈ log(sqrt(TemplateBox[{{1, -, {z, ^, 2}}}, Abs]) ⅇ^(1/2 ⅈ arg(1-z^2))+ⅈ z). ArcSin[z] has branch cut discontinuities in the complex plane.
  • Related mathematical functions include Sin, ArcCos, InverseHaversine, and ArcSinh.
Introduced in 1988
(1.0)