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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.
Note: Some authors [citation needed] define the range of arcsecant to be (< <), because the tangent function is nonnegative on this domain. This makes some computations more consistent.
Wikipedia says "Some authors define the range of arcsecant to be (0 ≤ y <π/2 or π ≤ y <3π/2), because the tangent function is nonnegative on this domain." It is likely that your course adheres to this convention (and you are requested to comply). Trig functions are not invertible -- trig functions do not have inverses.
15 cze 2021 · Substituting \(\sin(t) = \frac{1}{4x}\) gives \(\cos^{2}(t) + \left(\frac{1}{4x}\right)^2 = 1\). Solving, we get \[\cos(t) = \pm \sqrt{\frac{16x^2-1}{16x^2}} = \pm \frac{\sqrt{16x^2-1}}{4|x|}\] If \(t\) lies in \(\left(0, \frac{\pi}{2} \right]\), then \(\cos(t) \geq 0\), and we choose \(\cos(t) = \frac{\sqrt{16x^2-1}}{4|x|}\).
ArcSec[ z ] (2795 formulas) ArcSec : Visualizations (223 graphics, 1 animation) Plotting : Evaluation: Elementary Functions: ArcSec[z] (2795 formulas) Primary definition (1 formula) Specific values (32 formulas) General characteristics (13 formulas) Analytic continuations (0 formulas)
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!
