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asin

Compute the principal value of the arc sine of x, return in radians.

Base.asin — Method
asin(x::T) where {T <: Number} -> float(T)

Compute the inverse sine of x, where the output is in radians.

Return a T(NaN) if isnan(x).

See also asind for output in degrees.

Examples

julia> asin.((0, 1/2, 1))
(0.0, 0.5235987755982989, 1.5707963267948966)

julia> asind.((0, 1/2, 1))
(0.0, 30.000000000000004, 90.0)
source

Methods

julia> methods(asin, (Any,), [Base, Base.Math, Base.MathConstants, Base.MPFR])# 7 methods for generic function "asin" from Base:
 [1] asin(a::ComplexF16)
     @ math.jl:1527
 [2] asin(::Missing)
     @ math.jl:1548
 [3] asin(x::BigFloat)
     @ mpfr.jl:946
 [4] asin(a::Float16)
     @ math.jl:1526
 [5] asin(z::Complex)
     @ complex.jl:938
 [6] asin(x::T) where T<:Union{Float32, Float64}
     @ special/trig.jl:430
 [7] asin(x::Real)
     @ math.jl:1543

Examples

julia> using UnicodePlots
julia> lineplot(-1, 1, asin)           ┌────────────────────────────────────────┐
         2 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ asin(x)
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠃⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠁⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣀⠤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
   f(x)    │⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⠤⡷⠯⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠋⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⢀⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⢠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
        -2 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           └────────────────────────────────────────┘
           ⠀-1⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀1⠀
           ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀x⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Real Numbers

julia> asin.([-1.0, -0.5, 0.0, 0.5, 1.0])
5-element Vector{Float64}:
 -1.5707963267948966
 -0.5235987755982989
  0.0
  0.5235987755982989
  1.5707963267948966

julia> asin(-1.0) ≈ -asin(1.0)
true

julia> asin(0.5)*6 ≈ asin(1.0)*2 ≈ π
true

julia> asin(big"1")*2 == BigFloat(pi)
true

Complex

julia> asin(0-0im)
0.0 + 0.0im

julia> asin.(complex(-4:4))
9-element Vector{ComplexF64}:
 -1.5707963267948966 + 2.0634370688955608im
 -1.5707963267948966 + 1.762747174039086im
 -1.5707963267948966 + 1.3169578969248166im
 -1.5707963267948966 + 0.0im
                 0.0 + 0.0im
  1.5707963267948966 + 0.0im
  1.5707963267948966 + 1.3169578969248166im
  1.5707963267948966 + 1.762747174039086im
  1.5707963267948966 + 2.0634370688955608im

TODO: Complex3DPlot

Tips

  • Call asind for output in degrees.

See Also

asind, sin

Extended Inputs

Matrix

With Array like input:

julia> methods(asin, (Any,), [LinearAlgebra])# 5 methods for generic function "asin" from Base:
 [1] asin(D::Diagonal)
     @ /opt/hostedtoolcache/julia/1.12.2/x64/share/julia/stdlib/v1.12/LinearAlgebra/src/diagonal.jl:879
 [2] asin(J::UniformScaling)
     @ /opt/hostedtoolcache/julia/1.12.2/x64/share/julia/stdlib/v1.12/LinearAlgebra/src/uniformscaling.jl:176
 [3] asin(A::Hermitian{var"#s4811", S} where {var"#s4811"<:Complex, S<:(AbstractMatrix{<:var"#s4811"})})
     @ /opt/hostedtoolcache/julia/1.12.2/x64/share/julia/stdlib/v1.12/LinearAlgebra/src/symmetric.jl:929
 [4] asin(A::Union{Hermitian{T, S} where S, SymTridiagonal{T, V} where V<:AbstractVector{T}, Symmetric{T, S} where S} where T<:Real)
     @ /opt/hostedtoolcache/julia/1.12.2/x64/share/julia/stdlib/v1.12/LinearAlgebra/src/symmetric.jl:921
 [5] asin(A::AbstractMatrix)
     @ /opt/hostedtoolcache/julia/1.12.2/x64/share/julia/stdlib/v1.12/LinearAlgebra/src/dense.jl:1380
Base.asin — Method
asin(A::AbstractMatrix)

Compute the inverse matrix sine of a square matrix A.

If A is symmetric or Hermitian, its eigendecomposition (eigen) is used to compute the inverse sine. Otherwise, the inverse sine is determined by using log and sqrt. For the theory and logarithmic formulas used to compute this function, see [AH16_2].

Examples

julia> asin(sin([0.5 0.1; -0.2 0.3]))
2×2 Matrix{ComplexF64}:
  0.5-4.16334e-17im  0.1-5.55112e-17im
 -0.2+9.71445e-17im  0.3-1.249e-16im

Tech Notes

  • asin(::Number): by pure julia
  • asin(::BigFloat): by MPFR

Version History

Introduced in Julia v1.0 (2018)