acsc
Compute the principal value of the arc cosecant of x
, return in radians.
Base.Math.acsc
— Functionacsc(x)
Compute the inverse cosecant of x
, where the output is in radians.
acsc(A::AbstractMatrix)
Compute the inverse matrix cosecant of A
.
Methods
julia> methods(acsc, (Any,), [Base, Base.Math, Base.MathConstants, Base.MPFR])
# 1 method for generic function "acsc" from Base.Math: [1] acsc(y::Number) @ special/trig.jl:1157
Examples
julia> using UnicodePlots
julia> plot = Plot(; xlim=(-10, 10), ylim=(-pi/2, pi/2));
julia> lineplot!(plot, 1, 10, acsc);
julia> lineplot!(plot, -10, -1, acsc)
┌────────────────────────────────────────┐ 1.5708 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ acsc(x) │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ acsc(x) │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠙⠒⠲⠤⠤⢤⣀⣀⣀⣀⣀⣀⡀│ │⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭│ │⠈⠉⠉⠉⠉⠉⠉⠓⠒⠒⠢⠤⣄⣀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ -1.5708 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ └────────────────────────────────────────┘ ⠀-10⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀10⠀
Real Numbers
julia> acsc(Inf)
0.0
julia> acsc(-Inf)
-0.0
julia> acsc(1.0) / pi
0.5
julia> acsc(0)
ERROR: DomainError with Inf:
asin(x) is not defined for |x| > 1.
Stacktrace:
[...]
Complex
julia> acsc(Inf+0im)
0.0 - 0.0im
Tips
See Also
Extended Inputs
Matrix
With Array
like input:
julia> methods(acsc, (Any,), [LinearAlgebra])
# 3 methods for generic function "acsc" from Base.Math: [1] acsc(J::UniformScaling) @ LinearAlgebra /opt/hostedtoolcache/julia/1.11.5/x64/share/julia/stdlib/v1.11/LinearAlgebra/src/uniformscaling.jl:173 [2] acsc(D::Diagonal) @ LinearAlgebra /opt/hostedtoolcache/julia/1.11.5/x64/share/julia/stdlib/v1.11/LinearAlgebra/src/diagonal.jl:802 [3] acsc(A::AbstractMatrix{T}) where T @ LinearAlgebra /opt/hostedtoolcache/julia/1.11.5/x64/share/julia/stdlib/v1.11/LinearAlgebra/src/dense.jl:1365
Tech Notes
- Implemented in terms of
asin
:acsc(x) = inv(asin(x))
Version History
Introduced in Julia v1.0 (2018)