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The range of the trigonometric function sec x becomes the domain of sec inverse x, that is, (-∞, -1] U [1, ∞) and the range of arcsec function is [0, π/2) U (π/2, π]. Please note that sec inverse x is not the reciprocal of the trigonometric function secant x.
Domain of inverse function = Range of the function. So, domain of sin-1(x) is. [-1, 1] or -1 ≤ x ≤ 1. In the above table, the range of all trigonometric functions are given. From the fact, "Domain of inverse function = Range of the function", we can get the domain of all inverse trigonometric functions. Domain of sin-1(x) = [-1, 1]
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.
The domain and range of the inverse secant function, denoted as @$\begin{align*}sec^{-1}(x)\end{align*}@$ or @$\begin{align*}arcsec(x),\end{align*}@$ are as follows: Domain of sec-1 (x): @$\begin{align*} x \in (-\infty, -1] \cup [1, \infty) \end{align*}@$
16 wrz 2024 · Inverse trigonometric identities are mathematical expressions involving inverse trigonometric functions such as sin-1 (x), cos-1 (x), and tan-1 (x). These functions provide the angles (or arcs) corresponding to a given trigonometric ratio.
26 lis 2024 · The inverse secant sec^(-1)z (Zwillinger 1995, p. 465), also denoted arcsecz (Abramowitz and Stegun 1972, p. 79; Harris and Stocker 1998, p. 315; Jeffrey 2000, p. 124), is the inverse function of the secant.
3 paź 2022 · Recall from Section 5.2 that the inverse of a function \(f\) is typically denoted \(f^{-1}\). For this reason, some textbooks use the notation \(f^{-1}(x) = \cos^{-1}(x)\) for the inverse of \(f(x) = \cos(x)\). The obvious pitfall here is our convention of writing \((\cos(x))^2\) as \(\cos^{2}(x)\), \((\cos(x))^3\) as \(\cos^{3}(x)\) and so on.
