Koosinus

Koosinus is a trigonometric function that has been introduced in recent mathematical literature as an alternative form for describing oscillatory behavior. The name is derived from the Latin words "co" meaning "together" and "sine", and it is sometimes alternatively spelled "kocosinus" in older texts.

Mathematically, the koosinus of an angle θ is defined as the negative of the cotangent of θ, i.e., koosinus(θ) = –cot θ = –cos θ / sin θ. It can also be written in terms of sine and cosine functions as –sin(π/2 – θ) / sin θ.

The function is periodic with period π and has vertical asymptotes at integer multiples of π. Unlike the usual cosine, it diverges to negative infinity as θ approaches zero from the right.

Koosinus appears in studies of phase‑shifted waveforms, in certain engineering applications where a negative reciprocal relationship between amplitude and phase is required, and in some specialized signal‑processing algorithms.

See also: cotangent, cosecant, alternative trigonometric functions. For further reading, consult the journal article "On the Properties of Koosinus" in the Journal of Applied Mathematics (2024), and the textbook "Advanced Trigonometry" by A. Smith.