query: Why arsin function has range $[-\pi/2,\pi/2]$
positive_passages.docid: 73593
positive_passages.text: Why is the range of inverse trigonometric functions defined in this way?
negative_passages.docid: 17620
negative_passages.text: Why the principal value of complex number argument is taken within $(-\pi,\pi]?$
negative_passages.docid: 145521
negative_passages.text: Why does $\arctan(x)= \frac{1}{2i}\log \left( \frac{x-i}{x+i}\right)+k$?
negative_passages.docid: 60288
negative_passages.text: Why is $\arctan(x)=x-x^3/3+x^5/5-x^7/7+\dots$?
negative_passages.docid: 48252
negative_passages.text: Range of function Involving Modulus Quantity.
negative_passages.docid: 48086
negative_passages.text: Why is this series of square root of twos equal $\pi$?
negative_passages.docid: 95145
negative_passages.text: Does $\exp(2ir\pi)$ equal $1$? What's wrong?
negative_passages.docid: 88432
negative_passages.text: A problem on range of a trigonometric function: what is the range of $\frac{\sqrt{3}\sin x}{2+\cos x}$?
negative_passages.docid: 77669
negative_passages.text: Limits of trig functions
negative_passages.docid: 88097
negative_passages.text: Fourier series for $f(x)=(\pi -x)/2$
negative_passages.docid: 37642
negative_passages.text: Why is $\pi$ irrational if it is represented as $C/D$?
negative_passages.docid: 109900
negative_passages.text: Why is $e^{\pi \sqrt{163}}$ almost an integer?
negative_passages.docid: 4310
negative_passages.text: Range of $(a_{1}-a_{2})^2+(a_{2}-a_{3})^2+(a_{3}-a_{4})^2+(a_{4}-a_{1})^2$ is
negative_passages.docid: 124535
negative_passages.text: continuous function from $[\pi,2\pi]\to \mathbb{R}^2$
negative_passages.docid: 76490
negative_passages.text: Proving that $\cos(\arcsin(x))=\sqrt{1-x^2}$
negative_passages.docid: 24694
negative_passages.text: Why does a fourier series have a 1/2 in front of the a_0 coefficient
negative_passages.docid: 140300
negative_passages.text: Does the interval $[0,1]$ contains more real numbers than $(0,2)$?