Understanding the Tangent Function in Mathematics | Definition, Properties, and Graph

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In mathematics, tan(x) represents the tangent function, which is a trigonometric function that relates the angle x to the ratio of the length of the opposite side to the adjacent side of a right triangle

In mathematics, tan(x) represents the tangent function, which is a trigonometric function that relates the angle x to the ratio of the length of the opposite side to the adjacent side of a right triangle. Specifically, for a given angle x, the tangent of x is defined as the ratio of the length of the side opposite to the angle x (opposite side) to the length of the side adjacent to the angle x (adjacent side).

The tangent function can be expressed as:

tan(x) = opposite side / adjacent side

Alternatively, it can also be defined in terms of other trigonometric functions:

tan(x) = sin(x) / cos(x)

It is important to note that tangent is a periodic function, meaning its values repeat after certain intervals. The tangent function is undefined when the cosine of the angle x is equal to zero, which occurs at multiples of π/2 (90 degrees). At these points, the tangent function has vertical asymptotes.

The tangent function has a range from negative infinity to positive infinity. The graph of the tangent function is oscillatory and repetitive, with a vertical asymptote at every π/2 interval. It has points of zero where the sine function is zero, and it changes sign at each of these points.

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