## tangent

### ratio of the opposite to the adjacent side of a right-angled triangle

In trigonometry, the tangent is a trigonometric function that relates the opposite side and adjacent side of a right angle triangle. It is defined as the ratio of the length of the opposite side to the length of the adjacent side, i.e., Tanθ = Opposite/Adjacent.

The tangent function is commonly denoted as tan(θ), where θ represents the angle between the hypotenuse and the adjacent side of a right angle triangle. The value of the tangent function is always positive in the first and third quadrants and always negative in the second and fourth quadrants.

For example, if the angle is 30 degrees, then the tangent of 30 degrees can be calculated as follows:

Tan(30) = Opposite/Adjacent

Tan(30) = (1/2) / (√3/2)

Tan(30) = (1/2) x (2/√3)

Tan(30) = √3/3

Therefore, the tangent of 30 degrees is equal to √3/3. Similarly, we can find the tangent function for other angles as well. It is a useful trigonometric function that finds its applications in various fields such as engineering, physics, and mathematics.

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