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16 maj 2020 · Let's say we're looking for real number x whose arcsecant is angle θ. Then we have: θ = arcsec(x) sec(θ) = x 1 / cos(θ) = x cos(θ) = 1 / x θ = arccos(1/x) So with this reasoning, you can write your arcsecant function as: from math import acos def asec(x): return acos(1/x)
15 sty 2022 · For example, using this range, ( ()) =, whereas with the range (< <), we would have to write ( ()) =, since tangent is nonnegative on <, but nonpositive on <. For a similar reason, the same authors define the range of arccosecant to be ( − π < y ≤ − π 2 or 0 < y ≤ π 2 ) . {\displaystyle {\big (}-\pi <y\leq -{\tfrac {\pi ...
For example, using this range, ( ()) =, whereas with the range (< <), we would have to write ( ()) =, since tangent is nonnegative on <, but nonpositive on <. For a similar reason, the same authors define the range of arccosecant to be ( − π < y ≤ − π 2 {\textstyle (-\pi <y\leq -{\frac {\pi }{2}}} or 0 < y ≤ π 2 ...
12 sie 2024 · Range: \(\left[0, \frac{\pi}{2} \right) \cup \left(\frac{\pi}{2}, \pi\right]\) As \(x \to -\infty\), \(\mathrm{arcsec}(x) \to \frac{\pi}{2}^{+}\), and as \(x \to \infty\), \(\mathrm{arcsec}(x) \to \frac{\pi}{2}^{-}\) \(\sec\left(\mathrm{arcsec}(x)\right) = x\) provided \(|x| \geq 1\)
10 sie 2023 · If the range of arccosecant is taken to be \(\left[-\frac{\pi}{2}, 0\right) \cup \left(0, \frac{\pi}{2}\right]\), we can use Theorem \( \PageIndex{ 3 } \) to get \(\mbox{arccsc}\left(-\frac{3}{2}\right) = \arcsin\left(-\frac{2}{3}\right) \approx -0.7297\).
Using the inverse secant function, we would write this as: arcsec (2) = θ. This equation is read as “the arcsecant of 2 is equal to θ.” To solve this equation, we would take the inverse secant of 2, which means finding the angle whose secant value is 2. The result would give us the angle θ in radians or degrees.
The range of y = arcsec x. In calculus, sin −1 x, tan −1 x, and cos −1 x are the most important inverse trigonometric functions. Nevertheless, here are the ranges that make the rest single-valued. If x is positive, then the value of the inverse function is always a first quadrant angle, or 0.
