What is Arctan Formula?
Tangent is a trigonometric function and in a right-angled triangle, the tangent function equals the ratio of perpendicular and base (perpendicular/base).
Arctan is a reference to the inverse function of the tangent. Symbolically, arctan is represented by tan-1x in trigonometric equations.
Arctan Formula Definition
As discussed above, the basic formula for the arctan is given by, arctan (Perpendicular/Base) = θ, where θ is the angle between the hypotenuse and the base of a right-angled triangle. We use this formula for arctan to find the value of angle θ in terms of degrees or radians.
Suppose, the tangent of the angle θ equals x.
x = tan θ ⇒ θ = tan-1x
Let us take a right-angled triangle ABC with angle BCA as θ. Side AB is perpendicular(p) and side BC is base(b). Now, as we studied that tangent equals perpendicular by the base.
i.e. tan θ = Perpendicular/Base = p/b
And, by using the above expression,
θ = tan-1(p/b)
Arctan
Arctan is defined as the inverse of the tangent function. Arctan(x) is denoted as tan-1(x). There are six trigonometric functions and the inverse of all six functions is repressed as, sin-1x, cos-1x, tan-1x, cosec-1x, sec-1x, and cot-1x.
Arctan (tan-1x) is not similar to 1 / tan x. tan-1 x is the inverse of tan x whereas 1/ tan x is the reciprocal of tan x. tan-1 x is used to solve various trigonometric equations. In this article, we will study the arctan function formula, graph, properties, and others in detail.
Table of Content
- What is Arctan?
- What is Arctan Formula?
- Arctan Identities
- Arctan Domain and Range
- Arctan (x) Properties
- Arctan Table