Ratio between the
sine and the
cosine of an angle.
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: [latex]\sin \left( \theta \right) = y[/latex] and [latex]\cos \left( \theta \right) = x[/latex].
Therefore, [latex]\tan \left( \theta \right) = \dfrac{\sin \left( \theta \right)}{\cos \left( \theta \right)} = \dfrac {y}{x}[/latex]
Notation
The notation used to indicate the tangent of a real number x is “tan(x)” which is read as “the tangent of x.”
Example
In the
sexagesimal system of measuring angles, we have:
- tan(45) = 1
- tan(30) ≈ 0,577
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.”
