[tan.gent] adj [L tangent-, tangens, prp. of tangere to touch; perh. akin to OE thaccian to touch gently, stroke] (1594) 1 a: meeting a curve or surface in a single point if a sufficiently small interval is considered "straight line ~ to a curve" b (1): having a common tangent line at a point "~ curves" (2): having a common tangent plane at a point "~ surfaces"
2: diverging from an original purpose of course: irrelevant "~ remarks"
[2]tangent n [NL tangent-, tangens, fr. linea tangens tangent line] (1594) 1 a: the trigonometric function that for an acute angle is the ratio between the leg opposite to the angle when it is considered part of a right triangle and the leg adjacent b: a trigonometric function that is equal to the sine divided by the cosine for all real numbers A for which the cosine is not equal to zero and is exactly equal to the tangent of an angle of measure A in radians
2: a line that is tangent; specif: a straight line that is the limiting position of a secant of a curve through a fixed point and a variable point on the curve as the variable point approaches the fixed point--see circle illustration
3: an abrupt change of course: digression "the speaker went off on a ~"
4: a small upright flat-ended metal pin at the inner end of a clavichord key that strikes the string to produce the tone