"branch of mathematics that deals with relations between sides and angles of triangles," 1610s, from Modern Latin trigonometria (Barthelemi Pitiscus, 1595), from Greek trigonon "triangle" (from tri- "three" (see tri-) + gōnia "angle, corner" (from PIE root *genu- (1) "knee; angle") + metron "a measure" (from PIE root *me- (2) "to measure").

"pertaining to or depending upon the use of right angles," 1570s, from French orthogonal, from orthogone, from Late Latin orthogonius, from Greek orthogonios "right-angled," from ortho- "straight" (see ortho-) + gōnia "angle, corner" (from PIE root *genu- (1) "knee; angle"). Related: Orthogonally; orthogonality.

in trigonometry, "the tangent of the complement of a given angle," a contraction of co. tangent, abbreviation of complement + tangent (n.).