## Tangent

### In mathematics, the tangent is a trigonometric function that relates the angles of a right triangle to the ratio of the lengths of its sides

In mathematics, the tangent is a trigonometric function that relates the angles of a right triangle to the ratio of the lengths of its sides. More specifically, the tangent of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. The tangent function is denoted as “tan” and it is represented as:

tan(θ) = opposite/adjacent

Here, θ represents the angle of interest. It’s important to note that the tangent function is only defined for acute angles, as the side opposite the angle must be longer than the side adjacent to the angle. The tangent function is periodic with a period of π radians or 180 degrees.

The tangent function extends beyond right triangles and is widely used in various areas of mathematics, physics, engineering, and other fields. It is a fundamental trigonometric function that plays a significant role in calculating angles, distances, slopes, and rates of change. The tangent function is also helpful in the study of periodic phenomena, such as waves and vibrations.

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