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For a circle of radius 1, arcsin and arccos are the lengths of actual arcs determined by the quantities in question. Several notations for the inverse trigonometric functions exist.
7 paź 2023 · This calculator will find the inverse trigonometric values for principal values in the ranges listed in the table. You can view the ranges in the Inverse Trigonometric Function Graphs. Calculate Arcsine, Arccosine, Arctangent, Arccotangent, Arcsecant and Arccosecant for values of x and get answers in degrees, ratians and pi.
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, ∞).
15 cze 2021 · Domain: \([-1,1]\) Range: \(\left[ -\frac{\pi}{2}, \frac{\pi}{2}\right]\) \(\arcsin(x) = t\) if and only if \(-\frac{\pi}{2} \leq t \leq \frac{\pi}{2}\) and \(\sin(t) = x\) \(\sin(\arcsin(x)) = x\) provided \(-1 \leq x \leq 1\) \(\arcsin(\sin(x)) = x\) provided \(-\frac{\pi}{2} \leq x \leq \frac{\pi}{2}\) additionally, arcsine is odd
The domain of the arcsecant function is y ∈ (− ∞, − 1] ∪ [1, ∞), and the range is [0, π 2) ∪ (π 2, π]. This is because the secant function is not defined for x = π 2 + n π, where n is an integer, and the secant function is always greater than or equal to 1 or less than or equal to -1. Was this helpful? Ask your own question!
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