$\begingroup$ simple solution... draw a graph of the tangent function. Then draw the arctan function on both an x-y graph and a y-x graph. $\endgroup$ – John Joy

Apr 11, 2020 · Whenever I calculate inverse tangent on the calculator it only gives the correct angle when the point (X, Y) is in the first and fourth quadrant. Whenever the point lies in the …

By definition of the arctan function, as both sides have the same tangent, we only need to check under which condition $$-\frac\pi 2<\arctan u+\arctan v < \frac\pi2.$$ Let $\alpha=\arctan u$, …

$\begingroup$ I suppose your confussion stems from the fact that some pretty well-known scientific calculators (e.g., at least some of the Casio ones) denote by $\,\sin^{-1}\,,\,\cos^{ …

Apr 21, 2017 · How do you solve $\arctan(n)$ to radians by hand? I. e. $\arctan(1)$ >> process >> $\pi/4$ I have this Taylor expansion that allows me to calculate an approximate value for …

Nov 30, 2023 · I am trying to simplify $$\tan^{-1}\left(e^{ix}\right), x\in\mathbb{R}$$ $$=\\tan^{-1}\left(\cos x+i\sin x\right)$$ Using $$\tan^{-1}\left(a+b\right)=\frac12\tan^{-1 ...

The two functions resemble each other on the real line, but they're not the only sigmoidal functions around. . There are functions as simple as $\dfrac{x}{\sqrt{1+x^2}}$ and as …

While working on some probability question, I had to evaluate $\lim_{x \to \infty} \arctan(x)$. I knew the answer intuitively as $\pi/2$, yet I cannot figure out how to prove it by elementary …

Jun 10, 2016 · The reason that it isn't true is that, regrettably, the notation is not consistent. For this reason, many people avoid using $\tan^{-1}$ and use $\arctan$ instead, and so on for the …

Jan 14, 2017 · A quick google search of "java atan" would tell you that it stands for "arctangent", which is the inverse of tangent.