Tangent Function

The tangent function is one of the basic trigonometric functions and is quite a commonly used function in trigonometry. The tangent function can be expressed as the ratio of the sine function and cosine function. In a right-angled triangle, the formula for the tangent function is expressed as the ratio of the perpendicular and base of the triangle. It can also be expressed as the reciprocal of the cotangent function. Mathematically, tan function is written as f(x) = tan x

Further in this article, we will explore the tangent function graph, its domain and range, the trigonometric identities of tan x, and the formula of the tangent function. We will also solve some examples related to the tan function for a better understanding of the concept.

What is Tangent Function?

The tangent function is one of the main six trigonometric functions and is generally written as tan x. It is the ratio of the opposite side and the adjacent side of the angle in consideration in a right-angled triangle. We have various trigonometric identities and formulas related to the tangent function that can be derived using different formulas. The formula for the period of the tangent function f(x) = a tan (bx), is given by, Period = π/|b|. Tangent function tan x is a periodic function and has a period of π/1 = π (Because b =1 in tan x).

Tangent Function Formula

Now, we have two main formulas for the tangent function. As we know that, in a right-angled triangle, tan x is expressed as the ratio of the opposite side and the adjacent side of the angle in consideration. The tangent function can also be expressed as the ratio of the sine function and cosine function which can be derived using a unit circle. Hence, the formulas for tan x are:

• tan x = sin x/cos x
• tan x = Opposite Side/Adjacent Side = Perpendicular/Base