'assinuate' is a rare/variant form related to Latin 'insinuare', where 'in-' meant 'into' and 'sinus' meant 'fold, curve'.

'assinuate' appears as an analogical or variant form of Middle English forms of 'insinuate' (from Latin 'insinuare'), influenced by variation in prefix usage; it corresponds to modern 'insinuate' in sense and form.

Initially from Latin it meant 'to wind or thrust into a fold or opening' and later developed the sense 'to introduce or suggest gradually'; this evolved into the modern senses of 'to hint' or 'introduce subtly'.