In information technology, the function sees dedicated support in various high-performance math libraries (such as Intel's Math Kernel Library (MKL)[12] or MathCW[13]), available for many compilers and programming languages (including C, C++,[14] Common Lisp,[15][16] D,[17] Haskell,[18] Julia,[19] and Rust[20]).
Depending on the platform, the fused operation is about twice as fast as calling the sine and cosine functions individually.
If x and y are real, then The cis notation was first coined by William Rowan Hamilton in Elements of Quaternions (1866)[23][24] and subsequently used by Irving Stringham (who also called it "sector of x") in works such as Uniplanar Algebra (1893),[25][26] James Harkness and Frank Morley in their Introduction to the Theory of Analytic Functions (1898),[26][27] or by George Ashley Campbell (who also referred to it as "cisoidal oscillation") in his works on transmission lines (1901) and Fourier integrals (1928).
This can be rhetorically useful to mathematicians and engineers when discussing this function, and further serve as a mnemonic (for cos + i sin).
The usual proof that cis x = eix requires calculus, which the student may not have studied before encountering the expression cos x + i sin x.