1520s, "to covertly and subtly introduce into the mind or heart" (trans.), from Latin insinuatus, past participle of insinuare "to thrust in, push in, make a way; creep in, intrude, bring in by windings and curvings, wind one's way into," from in- "in" (from PIE root *en "in") + sinuare "to wind, bend, curve," from sinus "a curve, winding" (see sinus).
Intransitive meaning "hint obliquely" is from 1560s. Meaning "maneuver (someone or something) into some desired position or condition" is from 1570s. Physical or literal sense of "to introduce tortuously or indirectly" is from 1640s. Related: Insinuated; insinuating.
Others are reading
<a href="https://www.etymonline.com/word/sinuate">Etymology of sinuate by etymonline</a>
Harper, D. (n.d.). Etymology of sinuate. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/sinuate