Tangent

In trigonometry, the tangent of an angle in a right triangle is defined as the ratio of the opposite and adjacent sides. The tangent is a trigonometric function of the angle and is often abbreviated tan.

There is a relationship between the tangent and the sine and cosine functions:

<math>\tan \theta = \frac{\sin \theta}{\cos \theta} = \cot \left(\frac{\pi}{2} - \theta \right) = \frac{1}{\cot \theta} \,</math>

In analytic geometry, a line which intersects a circle or curve at only one point is said to be tangent to that circle or curve. At the point of intersection, the curve and the line have exactly the same slope.

Compare: Asymptote