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Tangent (of an angle)

The tangent of an angle is the trigonometric ratio between the adjacent side and the opposite side of a right triangle containing that angle.

$\text{tangent}=\frac{\text{length}\text{of}\text{the}\text{leg}\text{opposite}\text{to}\text{the}\text{angle}}{\text{length}\text{of}\text{the}\text{leg}\text{adjacent}\text{to}\text{the}\text{angle}}$ abbreviated as "tan"

The tangent ratio is the same regardless of the size of the right triangle. So, it is often easiest to consider a right triangle with a hypotenuse of length $1$ .

The tangent ratio can also be thought of as a function, which takes different values depending on the measure of the angle. You can measure an angle in degrees or  radians .

The reciprocal of the tangent ratio is known as cotangent ratio of an angle, abbreviated as "cot".

That is,

$\text{cotangent}=\frac{\text{length}\text{of}\text{the}\text{leg}\text{adjacent}\text{to}\text{the}\text{angle}}{\text{length}\text{of}\text{the}\text{leg}\text{opposite}\text{to}\text{the}\text{angle}}$

In the above example, $\cot \left(A\right)=\frac{7}{4}$ and $\cot \left(B\right)=\frac{4}{7}$ .

See also: sine and cosine .