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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.

tangent = length of the leg opposite to the angle length of the leg adjacent to the angle abbreviated as "tan"

Example:

In the triangle shown,

tan ( A ) = 6 8 or 3 4 and tan ( B ) = 8 6 or 4 3 .

Math diagram

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,

cotangent = length of the leg adjacent to the angle length of the leg opposite to the angle

In the above example, cot ( A ) = 7 4 and cot ( B ) = 4 7 .

See also: sine and cosine .

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