A trigonometric function that equals the reciprocal of the tangent, or the ratio of the adjacent side to the opposite side in a right triangle.
From Latin 'co-' meaning 'complementary' and 'tangent' from Latin 'tangens' meaning 'touching' (the line that touches a circle). It was named to reflect its relationship to the tangent function.
The 'co-' in cotangent, cosine, and cosecant represents a brilliant mathematical insight from Islamic and European mathematicians: the trig function of an angle equals the 'complementary' function of its complement angle, so they created a naming system to show that relationship.
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