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cos

Compute cosine of parameter in radians.

Methods

julia> methods(cos, (Any,), [Base, Base.Math, Base.MathConstants, Base.MPFR])# 8 methods for generic function "cos" from Base:
 [1] cos(x::BigFloat)
     @ Base.MPFR mpfr.jl:860
 [2] cos(a::Float16)
     @ Base.Math math.jl:1511
 [3] cos(::Irrational{:π})
     @ Base.MathConstants mathconstants.jl:147
 [4] cos(a::ComplexF16)
     @ Base.Math math.jl:1512
 [5] cos(::Missing)
     @ Base.Math math.jl:1533
 [6] cos(x::T) where T<:Union{Float32, Float64}
     @ Base.Math special/trig.jl:98
 [7] cos(x::Real)
     @ Base.Math math.jl:1528
 [8] cos(z::Complex{T}) where T
     @ complex.jl:912

Examples

julia> using UnicodePlots
julia> lineplot(0, 2π, cos)           ┌────────────────────────────────────────┐
         1 │⠉⠓⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠉⠀⠀⠀⠀│ cos(x)
           │⠀⠀⠈⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
   f(x)    │⠤⠤⠤⠤⠤⠤⠤⠤⠼⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
        -1 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⣀⣀⡤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           └────────────────────────────────────────┘
           ⠀0⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀7⠀
           ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀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)

See Also

cospi, sincos, cosd, cosh, acos

Extended Inputs

Matrix

With Array like input:

julia> methods(cos, (Any,), [LinearAlgebra])# 6 methods for generic function "cos" from Base:
 [1] cos(J::UniformScaling)
     @ LinearAlgebra /opt/hostedtoolcache/julia/1.11.2/x64/share/julia/stdlib/v1.11/LinearAlgebra/src/uniformscaling.jl:173
 [2] cos(D::Diagonal)
     @ LinearAlgebra /opt/hostedtoolcache/julia/1.11.2/x64/share/julia/stdlib/v1.11/LinearAlgebra/src/diagonal.jl:802
 [3] cos(A::Hermitian{var"#s5027", S} where {var"#s5027"<:Complex, S<:(AbstractMatrix{<:var"#s5027"})})
     @ LinearAlgebra /opt/hostedtoolcache/julia/1.11.2/x64/share/julia/stdlib/v1.11/LinearAlgebra/src/symmetric.jl:714
 [4] cos(A::Union{Hermitian{var"#s5028", S}, Symmetric{var"#s5028", S}} where {var"#s5028"<:Real, S})
     @ LinearAlgebra /opt/hostedtoolcache/julia/1.11.2/x64/share/julia/stdlib/v1.11/LinearAlgebra/src/symmetric.jl:710
 [5] cos(A::AbstractMatrix{<:Complex})
     @ LinearAlgebra /opt/hostedtoolcache/julia/1.11.2/x64/share/julia/stdlib/v1.11/LinearAlgebra/src/dense.jl:1022
 [6] cos(A::AbstractMatrix{<:Real})
     @ LinearAlgebra /opt/hostedtoolcache/julia/1.11.2/x64/share/julia/stdlib/v1.11/LinearAlgebra/src/dense.jl:1015
Missing docstring.

Missing docstring for cos(A::AbstractMatrix). Check Documenter's build log for details.

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 2018 (1.0)