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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.
15 sty 2022 · In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions are the inverse functions of the trigonometric functions (with suitably restricted domains).
Arcsecant's range comes from the arccosine's range. To make cosine invertible, the domain is restricted to [0, π] [0, π]. We will keep this restriction for secant as well. Note that since the range of cosine is [−1, 1] [− 1, 1], secant's range is always (−∞, −1) ∪ (1, ∞) (− ∞, − 1) ∪ (1, ∞).
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.
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The range of arcsecant: y∈ [0; π/2)∪ ( π/2; π]. Arcsecant is a non-periodic function. The arcsecant increases and is continuous on the interval x∈ (-∞; -1] and x∈ [1, + ∞), since the secant function (x= secy) is strictly increasing and continuous in the intervals [0; π/2) and (π/2;π]
15 cze 2021 · Our answer is \ (\arccos\left (-\frac {\sqrt {2}} {2}\right) = \frac {3\pi} {4}\). To find \ (\arcsin\left (-\frac {1} {2}\right)\), we seek the number \ (t\) in the interval \ (\left [-\frac {\pi} {2}, \frac {\pi} {2}\right]\) with \ (\sin (t) = -\frac {1} {2}\).
