Tangens

Part of speech: noun

Definitions

1. A mathematical function that represents the ratio of the length of the opposite side to the length of the adjacent side in a right triangle
2. A function used in trigonometry, defined as the sine divided by the cosine of an angle
3. An important concept in geometry and analysis, often appearing in various applications of calculus and periodic phenomena

Etymology: The Latin "tangens" means "touching," the present participle of "tangere," and it was coined as a technical term rather than arising from everyday speech. The name comes from the geometric picture: a tangent line touches a circle at a single point, and the line segment that runs from the circle's centre out to the tangent line, measured against the radius, gives the trigonometric ratio. Mathematicians used the Latin word to name that line, and the ratio took the same name. The Latin term entered the mathematical vocabulary through medieval and Renaissance work on trigonometry, where it became a standard name for the function. In English it appears as "tangent," the same Latin form, used in the same sense. Today the word is the English term for the ratio of the opposite side to the adjacent side in a right triangle, and it extends into calculus, where the derivative of the tangent function is the square of the secant.

Synonyms: tangents