`cot`

Compute the cotangent of x expressed in radians.

Base.Math.cot — Function

cot(x::T) where {T <: Number} -> float(T)

Compute the cotangent of x, where x is in radians.

Throw a DomainError if isinf(x), return a T(NaN) if isnan(x).

source

cot(A::AbstractMatrix)

Compute the matrix cotangent of a square matrix A.

Methods

julia> methods(cot, (Any,), [Base, Base.Math, Base.MathConstants, Base.MPFR])# 2 methods for generic function "cot" from Base.Math:
 [1] cot(::Irrational{:π})
     @ mathconstants.jl:150
 [2] cot(z::Number)
     @ special/trig.jl:1153

Examples

julia> using UnicodePlots
julia> lineplot(-2π, 2π, cot, xlim=(-7, 7), ylim=(-4, 4))           ┌────────────────────────────────────────┐
         4 │⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ cot(x)
           │⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡏⡆⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⡇⢣⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⡇⠈⡆⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⡇⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀│ 
   f(x)    │⠤⠤⠤⠤⠤⠬⠦⡤⠤⠤⠤⠤⠤⠤⠬⠦⡤⠤⠤⠤⡧⠤⠤⠬⠦⡤⠤⠤⠤⠤⠤⠤⠬⠦⡤⠤⠤⠤⠤⠤│ 
           │⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⡇⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⡇⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⡇⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠸⡀⡇⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀│ 
        -4 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀│ 
           └────────────────────────────────────────┘
           ⠀-7⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀7⠀
           ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀x⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Real Numbers

julia> cot(0)
Inf

julia> cot(-0.0)
-Inf

julia> cot(pi)
-Inf

julia> cot(pi/2)
6.123233995736766e-17

julia> cot(pi/4)
1.0000000000000002

Complex

julia> cot(0+0im)
NaN + NaN*im

Tips

Extended Inputs

Matrix

With Array like input:

julia> methods(cot, (Any,), [LinearAlgebra])# 3 methods for generic function "cot" from Base.Math:
 [1] cot(J::UniformScaling)
     @ /opt/hostedtoolcache/julia/1.12.2/x64/share/julia/stdlib/v1.12/LinearAlgebra/src/uniformscaling.jl:176
 [2] cot(D::Diagonal)
     @ /opt/hostedtoolcache/julia/1.12.2/x64/share/julia/stdlib/v1.12/LinearAlgebra/src/diagonal.jl:879
 [3] cot(A::AbstractMatrix{T}) where T
     @ /opt/hostedtoolcache/julia/1.12.2/x64/share/julia/stdlib/v1.12/LinearAlgebra/src/dense.jl:1496

Tech Notes

Implemented in terms of tan: cot(x) = inv(tan(x))

Version History

Introduced in Julia v1.0 (2018)