Understanding the Tangent Function: Definition, Calculation, and Properties

Tan(x)

The tangent function, often abbreviated as tan(x), is one of the three primary trigonometric functions

The tangent function, often abbreviated as tan(x), is one of the three primary trigonometric functions. It is defined as the ratio of the length of the side opposite to the angle x in a right triangle to the length of the adjacent side.

In simpler terms, tan(x) = opposite/adjacent.

To calculate the tangent of an angle, you first need to have the value of the angle. Then, you can use a scientific calculator or refer to the tangent table in mathematics to find its value.

For example, if you have an angle x = 45 degrees, you can calculate tan(x) as follows:

tan(45°) = opposite/adjacent.

In a right triangle with a 45° angle, the opposite and adjacent sides are equal in length. Let’s assume that both sides have a length of 1 unit.

Therefore, in this case, tan(45°) = 1/1 = 1.

So, the tangent of a 45-degree angle is equal to 1.

Keep in mind that the tangent function has some specific properties. It has a periodic nature with a period of π (pi). That means the value of tan(x) repeats itself every 180 degrees or π radians. Additionally, tan(x) is undefined when x is equal to 90° + n * 180°, where n is an integer. This is because the tangent of a right angle is undefined.

I hope this explanation helps! If you have any further questions, feel free to ask.

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