`cos`

Compute the cosine of x expressed in radians.

Base.cos — Function

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

Compute cosine of x, where x is in radians.

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

See also cosd, cospi, sincos, cis.

source

cos(A::AbstractMatrix)

Compute the matrix cosine of a square matrix A.

If A is symmetric or Hermitian, its eigendecomposition (eigen) is used to compute the cosine. Otherwise, the cosine is determined by calling exp.

Examples

julia> cos(fill(1.0, (2,2)))
2×2 Matrix{Float64}:
  0.291927  -0.708073
 -0.708073   0.291927

Methods

julia> methods(cos, (Any,), [Base, Base.Math, Base.MathConstants, Base.MPFR])# 8 methods for generic function "cos" from Base:
 [1] cos(a::ComplexF16)
     @ math.jl:1527
 [2] cos(::Missing)
     @ math.jl:1548
 [3] cos(x::BigFloat)
     @ mpfr.jl:946
 [4] cos(a::Float16)
     @ math.jl:1526
 [5] cos(::Irrational{:π})
     @ mathconstants.jl:147
 [6] cos(z::Complex{T}) where T
     @ complex.jl:912
 [7] cos(x::T) where T<:Union{Float32, Float64}
     @ special/trig.jl:98
 [8] cos(x::Real)
     @ math.jl:1543

Examples

julia> using UnicodePlots
julia> lineplot(-π, π, cos)           ┌────────────────────────────────────────┐
         1 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠉⡏⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ cos(x)
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⡇⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⡇⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⡇⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
   f(x)    │⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠧⠤⠤⠤⠤⠤⠤⠤⡧⠤⠤⠤⠤⠤⠤⠼⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀│ 
        -1 │⠀⠀⠀⠀⣀⡠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⡀⠀⠀⠀⠀│ 
           └────────────────────────────────────────┘
           ⠀-4⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀4⠀
           ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀x⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Real Numbers

julia> cos(0)
1.0

julia> cos(0.5*pi)
6.123233995736766e-17

julia> cos(pi)
-1.0

julia> pi
π = 3.1415926535897...

julia> cos.([0 0.5*pi pi 1.5*pi 2*pi])
1×5 Matrix{Float64}:
 1.0  6.12323e-17  -1.0  -1.83697e-16  1.0

big float, cos(pi/2) == 0:

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

julia> cos(pi/big"2")
5.48458720489676038371065313197849010525379118254343975589502858496071344256677e-78

Complex

julia> cos(0+0im)
1.0 - 0.0im

plot real part

julia> using UnicodePlots
julia> cos_real(x, y) = real(cos(x + y*im))cos_real (generic function with 1 method)
julia> surfaceplot(-2pi:0.01:2pi, -pi:0.01:pi, cos_real)    ┌────────────────────────────────────────┐  10
    │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ ┌──┐
    │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ │▄▄│
    │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣰⠆⠀⠀⠀⠀⠀│ │▄▄│
    │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀│ │▄▄│
    │⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣄⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀│ │▄▄│
    │⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣆⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀│ │▄▄│
    │⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀│ │▄▄│
    │⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀│ │▄▄│
    │⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠈⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀│ │▄▄│
    │⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠙⠛⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀│ │▄▄│
    │⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀│ │▄▄│
    │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠙⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀│ │▄▄│
    │⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ │▄▄│
    │⠀⢀⡠⠼⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ │▄▄│
    │⠊⠁⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ └──┘
    └────────────────────────────────────────┘ -10

Tips

Call cospi to compute cos(x*pi)

Extended Inputs

Matrix

With Array like input:

julia> methods(cos, (Any,), [LinearAlgebra])# 6 methods for generic function "cos" from Base:
 [1] cos(D::Diagonal)
     @ /opt/hostedtoolcache/julia/1.12.2/x64/share/julia/stdlib/v1.12/LinearAlgebra/src/diagonal.jl:879
 [2] cos(J::UniformScaling)
     @ /opt/hostedtoolcache/julia/1.12.2/x64/share/julia/stdlib/v1.12/LinearAlgebra/src/uniformscaling.jl:176
 [3] cos(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:898
 [4] cos(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:894
 [5] cos(A::AbstractMatrix{<:Complex})
     @ /opt/hostedtoolcache/julia/1.12.2/x64/share/julia/stdlib/v1.12/LinearAlgebra/src/dense.jl:1125
 [6] cos(A::AbstractMatrix{<:Real})
     @ /opt/hostedtoolcache/julia/1.12.2/x64/share/julia/stdlib/v1.12/LinearAlgebra/src/dense.jl:1116

julia> cos([1 2; 3 4])
2×2 Matrix{Float64}:
  0.855423  -0.110876
 -0.166315   0.689109

julia> cos.([1 2; 3 4])
2×2 Matrix{Float64}:
  0.540302  -0.416147
 -0.989992  -0.653644

julia> cos([1 2; 3 4]) == cos.([1 2; 3 4])
false

Tech Notes

cos(::Number): by pure julia
cos(::BigFloat): by MPFR

Version History

Introduced in Julia v1.0 (2018)