std::sin(std::complex)(3)

✨ NAME ✨

okay so bestie, this is std::sin(std::complex)(3) from the C++ Standard Libary — section 3, she’s official, manual name folded in right here. The NAME is literally std::sin(std::complex) - std::sin(std::complex). no cap, that’s the whole label. 🫶

🌸 Synopsis 🌸

Defined in header <complex>:

template< class T >
complex<T> sin( const complex<T>& z );

Computes complex sine of a complex value z. That’s the assignment, and she ate. 💅

💅 Parameters 💅

• z — complex value. That’s it. That’s the parameter. 🎀

✨ Return value ✨

If no errors occur, the complex sine of z is returned. periodt. 💖

Errors and special cases are handled as if the operation is implemented by -i * std::sinh(i * z), where i is the imaginary unit. Keep that exactly in your notes, bestie — it’s giving main character math. 🦋

🦋 Notes 🦋

The sine is an entire function on the complex plane, and has no branch cuts. iconic behavior, honestly. ✨

Mathematical definition of the sine is:

sin z =

eiz
-e-iz
2i

.

🎀 Example 🎀

// Run this code

#include <cmath>
#include <complex>
#include <iostream>

int main()
{
    std::cout << std::fixed;
    std::complex<double> z(1.0, 0.0); // behaves like real sine along the real line
    std::cout << "sin" << z << " = " << std::sin(z)
              << " ( sin(1) = " << std::sin(1) << ")\n";

    std::complex<double> z2(0.0, 1.0); // behaves like sinh along the imaginary line
    std::cout << "sin" << z2 << " = " << std::sin(z2)
              << " (sinh(1) = " << std::sinh(1) << ")\n";
}

🌈 Output: 🌈

sin(1.000000,0.000000) = (0.841471,0.000000) ( sin(1) = 0.841471)
sin(0.000000,1.000000) = (0.000000,1.175201) (sinh(1) = 1.175201)

👑 See also 👑

• cos(std::complex) — computes cosine of a complex number (cos(z)) (function template).
• tan(std::complex) — computes tangent of a complex number (tan(z)) (function template).
• asin(std::complex) — computes arc sine of a complex number (C++11) (arcsin(z)) (function template).
• sin — computes sine (sin(x)) (function).
• sinf — computes sine (sin(x)) (function, C++11).
• sinl — computes sine (sin(x)) (function, C++11).
• sin(std::valarray) — applies the function std::sin to each element of valarray (function template).
• C documentation for csin

xoxo, your complex-sine stan 💜 — this page’s source is http://cppreference.com, version/date is 2024.06.10, and the footer tag is std::sin(std::complex)(3) 🫶✨