Consider a right triangle with a hypotenuse that measures 1 unit, or a trigonometric circle in which

*r*= 1.In this right triangle, we have the relations: \(\sin \left( \theta \right) = y\) and \(\cos \left( \theta \right) = x\).

Therefore, \(\tan \left( \theta \right) = \dfrac{\sin \left( \theta \right)}{\cos \left( \theta \right)} = \dfrac {y}{x}\)

### Notation

The notation used to indicate the tangent of a real number *x* is “tan(*x*)” which is read as “the tangent of *x*.”

### Educational Note

It should be noted that the argument of the tangent is a number (a measurement) and not a geometric figure (an angle). It’s a linguistic shortcut to use the expression “tangent of an angle” to express the “tangent of the measure of an angle.”