sec
Compute the secant of x
expressed in radians.
Base.Math.sec
— Functionsec(x)
Compute the secant of x
, where x
is in radians.
sec(A::AbstractMatrix)
Compute the matrix secant of a square matrix A
.
Methods
julia> methods(sec, (Any,), [Base, Base.Math, Base.MathConstants, Base.MPFR])
# 2 methods for generic function "sec" from Base.Math: [1] sec(x::BigFloat) @ Base.MPFR mpfr.jl:860 [2] sec(z::Number) @ special/trig.jl:1135
Examples
julia> using UnicodePlots
julia> lineplot(-2π, 2π, sec, xlim=(-7, 7), ylim=(-4, 4))
┌────────────────────────────────────────┐ 4 │⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀│ sec(x) │⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⡇⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀│ │⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀│ │⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⡇⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀│ │⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡇⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀│ │⠀⠀⠤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡧⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠀⠀│ │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ f(x) │⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤│ │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ │⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⢤⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡤⠒⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀│ │⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀│ │⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀│ │⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀│ │⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀│ -4 │⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀│ └────────────────────────────────────────┘ ⠀-7⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀7⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀x⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
Real Numbers
julia> sec(0)
1.0
julia> sec(pi)
-1.0
julia> sec(pi/4)
1.414213562373095
julia> sec(pi/3)
1.9999999999999996
julia> sec(pi/2)
1.633123935319537e16
Complex
julia> sec(0+0im)
1.0 + 0.0im
Tips
See Also
Extended Inputs
Matrix
With Array
like input:
julia> methods(sec, (Any,), [LinearAlgebra])
# 3 methods for generic function "sec" from Base.Math: [1] sec(J::UniformScaling) @ LinearAlgebra /opt/hostedtoolcache/julia/1.11.5/x64/share/julia/stdlib/v1.11/LinearAlgebra/src/uniformscaling.jl:173 [2] sec(D::Diagonal) @ LinearAlgebra /opt/hostedtoolcache/julia/1.11.5/x64/share/julia/stdlib/v1.11/LinearAlgebra/src/diagonal.jl:802 [3] sec(A::AbstractMatrix{T}) where T @ LinearAlgebra /opt/hostedtoolcache/julia/1.11.5/x64/share/julia/stdlib/v1.11/LinearAlgebra/src/dense.jl:1348
Tech Notes
- Implemented in terms of
cos
:sec(x) = inv(cos(x))
Version History
Introduced in Julia v1.0 (2018)