**Tangent** is a trigonometric ratio. In a right triangle with an angle ,

is the side of the triangle not part of angle , and is the side that is.

## Proof

The proof that is one of the most simple proofs around. We know that and . Dividing them gives which is also equal to .

## Properties

The tangent of an angle is the sine of said angle divided by cosine.

The reciprocal of tangent is cotangent (abbreviated as ), while its inverse is or . Note that tangent is not being raised to the power of -1; this is an inverse function, not a reciprocal.

The derivative of is , while its antiderivative is .

The derivative of is