Tangent of an Angle

Tangent of an Angle

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: \(\sin \left( \theta \right) = y\) and \(\cos \left( \theta \right) = x\).

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


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


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.”

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