/ˈsɪnjueɪt/
[adjective] Having a wavy or curved edge or outline, especially used in biology to describe the wavy-edged margins of leaves, shells, or other natural forms. It can also be used as a verb meaning to move in a winding or curving way.
Every winding river, every wavy leaf edge, and every sinuous dancer owes their description to the Latin word for a curve in a ship's sail.
The word 'sinuate' traces its origins to the Latin noun 'sinus', a word of remarkable flexibility that originally referred to the curved fold or pocket of a Roman toga, the kind of loose, billowing fold of cloth that a Roman citizen might gather at his chest or use as a makeshift bag. From this very physical image of folded fabric, 'sinus' extended to mean any kind of bay, curve, or hollow — including geographical bays, the curves of a winding river, and the hollow spaces inside the body, which is why we still call the air-filled cavities in our skulls 'sinuses' to this day.
From the noun 'sinus', Latin speakers formed the verb 'sinuare', meaning to bend, to curve, or to wind — to give something the shape of that characteristic fold. Latin 'sinuare' then produced the participial adjective 'sinuatus', meaning having been curved or having a wavy form. English borrowed this directly as 'sinuate' in the 17th century, and the word arrived almost fully formed, needing little change because English was already well acquainted with borrowing Latin scientific and botanical vocabulary wholesale during the great expansion of natural history writing.
In English, 'sinuate' found its most comfortable home in the language of botany and natural history. When 18th and 19th century naturalists needed precise terms to describe the edges of leaves, the outlines of shells, or the contours of insect wings, 'sinuate' proved enormously useful. A sinuate leaf margin is one that curves gently in and out in broad, smooth waves — not sharply toothed, not perfectly smooth, but gracefully undulating, like the memory of that original folded toga still breathing through the language.
The Latin root 'sinus' gave English a rich family of related words through different pathways. Directly from Latin, English gained 'sinus' itself (the anatomical hollow), 'sinuous' (winding and graceful, via Latin 'sinuosus'), and 'sinuosity' (the quality of being winding). The mathematical term 'sine' — the trigonometric function used to describe wave-like relationships — came into English via Medieval Latin 'sinus', which was used as a translation of the Arabic word 'jayb' (meaning a fold or pocket), which itself was used to translate the Sanskrit mathematical term 'jīvā'. So from Latin 'sinus' → Medieval Latin 'sinus' (mathematical) → English 'sine', we trace a word that connects Roman clothing to global mathematics.
Perhaps the most elegant of 'sinus's descendants is 'insinuate', which arrived in English in the 16th century from Latin 'insinuare', meaning literally to wind oneself into something or to introduce by curving in. The path was Latin 'insinuare' → English 'insinuate'. To insinuate was originally to slip into a place the way a river bends and finds its way into a landscape — gradually, smoothly, without force. Over time, the word took on its now-dominant sense of suggesting something indirectly or planting an idea in someone's mind with subtle cunning. A word born from the innocent curve of a toga's fold had learned to whisper.