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sin

Compute the sine of x expressed in radians.

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

Compute sine of x, where x is in radians.

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

See also sind, sinpi, sincos, cis, asin.

Examples

julia> round.(sin.(range(0, 2pi, length=9)'), digits=3)
1×9 Matrix{Float64}:
 0.0  0.707  1.0  0.707  0.0  -0.707  -1.0  -0.707  -0.0

julia> sind(45)
0.7071067811865476

julia> sinpi(1/4)
0.7071067811865475

julia> round.(sincos(pi/6), digits=3)
(0.5, 0.866)

julia> round(cis(pi/6), digits=3)
0.866 + 0.5im

julia> round(exp(im*pi/6), digits=3)
0.866 + 0.5im
source
sin(A::AbstractMatrix)

Compute the matrix sine of a square matrix A.

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

Examples

julia> sin(fill(1.0, (2,2)))
2×2 Matrix{Float64}:
 0.454649  0.454649
 0.454649  0.454649

Methods

julia> methods(sin, (Any,), [Base, Base.Math, Base.MathConstants, Base.MPFR])# 8 methods for generic function "sin" from Base:
 [1] sin(a::ComplexF16)
     @ math.jl:1527
 [2] sin(::Missing)
     @ math.jl:1548
 [3] sin(x::BigFloat)
     @ mpfr.jl:946
 [4] sin(a::Float16)
     @ math.jl:1526
 [5] sin(::Irrational{:π})
     @ mathconstants.jl:146
 [6] sin(z::Complex{T}) where T
     @ complex.jl:894
 [7] sin(x::T) where T<:Union{Float32, Float64}
     @ special/trig.jl:29
 [8] sin(x::Real)
     @ math.jl:1543

Examples

julia> using UnicodePlots
julia> lineplot(-π, π, sin)           ┌────────────────────────────────────────┐
         1 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡠⠚⠉⠉⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ sin(x)
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡜⠁⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀│ 
   f(x)    │⠤⠤⠤⠤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠵⠤⠤⠤⠤│ 
           │⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           │⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
        -1 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀⣀⡤⠊⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ 
           └────────────────────────────────────────┘
           ⠀-4⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀4⠀
           ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀x⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Real Numbers

julia> sin(0)
0.0

julia> sin(0.5*pi)
1.0

julia> sin(pi)
0.0

julia> pi
π = 3.1415926535897...

julia> sin.([0 0.5*pi pi 1.5*pi 2*pi])
1×5 Matrix{Float64}:
 0.0  1.0  1.22465e-16  -1.0  -2.44929e-16
dot-style function call

f.(args) means eval args one by one.

big float, sin(pi/6) == sin(30°) == 1/2:

julia> sin(pi/6)
0.49999999999999994

julia> sin(pi/big"6")
0.4999999999999999999999999999999999999999999999999999999999999999999999999999957

special float NaN, Inf:

julia> sin(NaN)
NaN

julia> sin(Inf)
ERROR: DomainError with Inf:
sin(x) is only defined for finite x.
[...]

Complex

julia> sin(0+0im)
0.0 + 0.0im

plot real part

julia> using UnicodePlots
julia> sin_real(x, y) = real(sin(x + y*im))sin_real (generic function with 1 method)
julia> surfaceplot(-2pi:0.01:2pi, -pi:0.01:pi, sin_real)    ┌────────────────────────────────────────┐  10
    │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ ┌──┐
    │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ │▄▄│
    │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀│ │▄▄│
    │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡀⠀⠀⠀⠀⢠⣿⣿⡀⠀⠀⠀⠀⠀⠀│ │▄▄│
    │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⣼⣿⣿⣇⠀⠀⠀⠀⠀⠀│ │▄▄│
    │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀│ │▄▄│
    │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣧⣀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠉⠛⠃⠀⠀⠀⠀⠀│ │▄▄│
    │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ │▄▄│
    │⠀⠀⠀⠀⠀⢠⣤⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠉⢻⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ │▄▄│
    │⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ │▄▄│
    │⠀⠀⠀⠀⠀⠀⢹⣿⣿⡟⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ │▄▄│
    │⠀⠀⠀⠀⠀⠀⠈⣿⣿⠃⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ │▄▄│
    │⠀⠀⠀⢸⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ │▄▄│
    │⠀⢀⡠⠼⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ │▄▄│
    │⠊⠁⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ └──┘
    └────────────────────────────────────────┘ -10

Tips

  • Call sinpi to compute sin(x*pi)

See Also

sinpi, sincos, sind, sinh, asin

Extended Inputs

Matrix

With Array like input:

julia> methods(sin, (Any,), [LinearAlgebra])# 6 methods for generic function "sin" from Base:
 [1] sin(D::Diagonal)
     @ /opt/hostedtoolcache/julia/1.12.2/x64/share/julia/stdlib/v1.12/LinearAlgebra/src/diagonal.jl:879
 [2] sin(J::UniformScaling)
     @ /opt/hostedtoolcache/julia/1.12.2/x64/share/julia/stdlib/v1.12/LinearAlgebra/src/uniformscaling.jl:176
 [3] sin(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] sin(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] sin(A::AbstractMatrix{<:Complex})
     @ /opt/hostedtoolcache/julia/1.12.2/x64/share/julia/stdlib/v1.12/LinearAlgebra/src/dense.jl:1165
 [6] sin(A::AbstractMatrix{<:Real})
     @ /opt/hostedtoolcache/julia/1.12.2/x64/share/julia/stdlib/v1.12/LinearAlgebra/src/dense.jl:1156
julia> sin([1 2; 3 4])
2×2 Matrix{Float64}:
 -0.465581  -0.148424
 -0.222637  -0.688218

julia> sin.([1 2; 3 4])
2×2 Matrix{Float64}:
 0.841471   0.909297
 0.14112   -0.756802

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

Tech Notes

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

Version History

Introduced in Julia v1.0 (2018)