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In mathematics, the inverse trigonometric functions (occasionally also called antitrigonometric, [1] cyclometric, [2] or arcus functions [3]) are the inverse functions of the trigonometric functions, under suitably restricted domains.
18 lut 2024 · Arctan (tan-1 x) 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.
Arctangent, written as arctan or tan -1 (not to be confused with ) is the inverse tangent function. The graph of y = arctan (x) is shown below. The domain of y = arctan (x) is all x values and its range is . One of the properties of inverse functions is that if a point (a, b) is on the graph of f, the point (b, a) is on the graph of its inverse.
Arcus tangens x jest definiowany jako odwrotna funkcja styczna x, gdy x jest rzeczywiste (x ∈ℝ ). Gdy styczna y jest równa x: Wtedy arcus tangens x jest równy odwrotnej funkcji stycznej x, która jest równa y: arctan (x), tan-1 (x), odwrotna funkcja styczna.
Arctan 1 (or tan inverse 1) gives the angle measure of a right-angled triangle in which the ratio of the opposite side and the adjacent side to the angle is equal to 1. The value of arctan 1 is 45° or π/4 radians.
\[\tan^2(x)=(\tan(x))^2=\tan(x)\cdot \tan(x) \nonumber \] Therefore, \(\tan^{-1}(x)\) is the inverse function of \(\tan(x)\) with respect to the composition operation, whereas \(\tan^2(x)\) is the square with respect to the usual product in \(\mathbb{R}\).
