std::cos(std::complex)(3)

💖 std::cos(std::complex)(3) 💖

okay so bestie, this page is from the C++ Standard Libary manual — yes, “Libary” exactly like that, we are not correcting the icon — and it’s the std::cos(std::complex) page. It’s giving “cosine but make it complex,” and honestly the math girlies ate. 🫶✨

💅 NAME 💅

std::cos(std::complex) — std::cos(std::complex)

✨ Synopsis ✨

Defined in header <complex>:

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

Computes complex cosine of a complex value z. 😌✨

🌸 Parameters 🌸

• z — complex value

🎀 Return value 🎀

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

Errors and special cases are handled as if the operation is implemented by std::cosh(i * z), where i is the imaginary unit. 🌀

🦋 Notes 🦋

The cosine is an entire function on the complex plane, and has no branch cuts. No cap, that’s iconic. ✨

Mathematical definition of the cosine is cos z = a fraction: eiz and +e-iz over 2. 🧮💅 The manpage lays it out like a little math stack; those exact bits are eiz, +e-iz, and 2.

🍓 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 cosine along
       the real line
            std::cout << "cos" << z << " = " << std::cos(z)
                      << " ( cos(1) = " << std::cos(1) << ")\n";

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

💜 Output: 💜

cos(1.000000,0.000000) = (0.540302,-0.000000) ( cos(1) = 0.540302)
cos(0.000000,1.000000) = (1.543081,-0.000000) (cosh(1) = 1.543081)

🔥 See also 🔥

• sin(std::complex) — computes sine of a complex number (\({\small\sin{z}}\)sin(z)) (function template)
• tan(std::complex) — computes tangent of a complex number (\({\small\tan{z}}\)tan(z)) (function template)
• acos(std::complex) — (C++11) computes arc cosine of a complex number (\({\small\arccos{z}}\)arccos(z)) (function template)
• cos, cosf, cosl — computes cosine (\({\small\cos{x}}\)cos(x)) ((function)); the page also lists (C++11) and (C++11) right here. 🫶
• cos(std::valarray) — applies the function std::cos to each element of valarray (function template)
• C documentation for ccos — the C cousin is right there in the references.

okay that’s the whole page, bestie — source/version and date at the very end: http://cppreference.com, 2024.06.10, page std::cos(std::complex)(3). Mwah 💋✨