What does cosine mean?
The cosine is one of the fundamental trigonometric functions, alongside sine and tangent. In its most elementary form, it relates the angles and sides of a right triangle: the cosine of an acute angle is the length of the side adjacent to that angle divided by the length of the hypotenuse. More generally, cosine extends to all real numbers as a periodic function — the x-coordinate traced by a point moving around the unit circle — producing the smooth, repeating wave familiar from physics and signal processing. Engineers use it to resolve forces into components, physicists use it to describe oscillations and waves, and programmers rely on it in graphics and audio algorithms. The word entered English in the early seventeenth century, formed from "co-" (complementary) plus "sine," because the cosine of an angle equals the sine of its complement. Compact, precise, and indispensable, "cosine" belongs to the small set of mathematical terms that appear everywhere from classroom geometry to modern technology.
nounIn trigonometry, the ratio of the side adjacent to an acute angle in a right triangle to the hypotenuse; equivalently, for any real number x, the x-coordinate of the point on the unit circle at angle x.
- In trigonometry, the ratio of the adjacent side to the hypotenuse in a right triangle containing a given acute angle.
- As a periodic real-valued function, cos x gives the x-coordinate of the point where the terminal side of angle x meets the unit circle; used throughout mathematics, physics, and engineering to model waves and oscillations.
"The engineer used the law of cosines to calculate the length of the third side of the triangular plot."
"To find the horizontal component of the force, multiply its magnitude by the cosine of the launch angle."
"A cosine wave describes how alternating current varies smoothly over time."
The plural refers to multiple cosine values or to the function applied to several angles, as in tabulating the cosines of a range of angles.
"The table lists the sines and cosines of every degree from zero to ninety."
The "co" in cosine literally means "complement" — it was invented as the sine of the complementary angle before anyone thought to define it on its own.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of cosine
The term "cosine" originated in early-seventeenth-century European mathematics, when trigonometric tables listed the sine of each complementary angle under the abbreviation "co. sinus." The English mathematician Edmund Gunter is often credited with popularizing this contraction, which later solidified into the single word "cosinus" and then "cosine." Both elements are Latin: "co-" means "complementary," and "sinus" originally meant a fold, hollow, or bosom — the same Latin word that gave us "sinus" in anatomy, "sinuous," and "insinuate." Thus "cosine" and "sine" are sibling coinages from the shared root "sinus."
Usage notes
Strictly technical vocabulary, confined almost entirely to mathematics, physics, engineering, and computing; it carries no figurative or everyday sense. In writing, it is frequently abbreviated as "cos". The plural "cosines" refers to multiple such values or functions, e.g. across several angles.
Don't confuse with
"Cosine" is a trigonometric function, while "cosign" (or "co-sign") means to sign a document jointly with another person, as on a loan.