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It only equals $\theta $ if $$-\frac {\pi}{2}<\theta < \frac {\pi}{2} $$ as the range of $\arctan$ is only from $-\frac {\pi}{2} $ to $\frac {\pi}{2} $. If $\theta $ is outside this interval, then you would need to add or subtract $\pi $ from $\theta $ until you get to the angle in this interval that has the same value of $\tan$.

2016年12月27日 · As we want $\arctan$ to be a function, we have to choose a range of output values. When you use the $\arctan$ to get the polar angle, there is an uncertainty of $\pi$ because $\tan (x+\pi)=\tan x$. You have to use the real and imaginary parts to decide the multiple of $\pi$ to add to the $\arctan$ output to get the proper polar angle you want.

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$\begingroup$ 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 $\,\sin^{-1}\,,\,\cos^{-1}\,,\,\tan^{-1}\,$ the inverse trigonometric functions...a very poor, sloppy choice by those Casio guys, and since these calculators are very widely used by high school students and these …

2017年4月21日 · Converting to radians gives $\mathrm{arctan}(1)=\pi/4$. Finding the exact arctangent of other values would be much more complicated, though you ought to be able to estimate the arctangent by picturing it. For example, it's easy to estimate that $\mathrm{arctan}(1/3)$ should be about $15$ or $20$ degrees, just by picturing a line with …

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2022年8月23日 · I know couple of formulas for trigonometric functions. But I don't know if such formulas exists for inverse trigonometric functions. I don't have a clue where to start with. Any hint will be apprec...

2018年5月29日 · I tried searching for how you derive the integral/primitive of $\\arctan(x)$, but I can't find any question on S.E with an answer that clearly explains this. I feel that there should be one, since i...

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