Final answer:
In mathematics, the word 'tangent' denotes a line that gently touches a curve at exactly one point, or in trigonometry, it is a ratio relating the lengths of sides in a right-angled triangle.
Step-by-step explanation:
The word tangent has its origin in the Latin root tactus, which means 'to touch'. In mathematics, a tangent typically refers to a line that touches a curve at a single point without crossing over it. This concept is extensively used in geometry, particularly when discussing circles and other curved figures. When a line is tangent to a circle, it intersects the circle's circumference at exactly one point. Moreover, in trigonometry, the tangent refers to a ratio derived from a right-angled triangle, defined as the opposite side over the adjacent side, which is the basis for the function tan(theta).