User:PCMorphy72/math: Difference between revisions

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Formula without apparent conditional construct: $\operatorname {atan2} (y,x)=\lim _{z\to x^{+}}\arctan \left({\frac {y}{z}}\right)+{\frac {\pi }{2}}\operatorname {sgn}(y)\operatorname {sgn}(x)\left(\operatorname {sgn}(x)-1\right)$

, that is useful e.g. to define the multivalued version of each inverse trigonometric function: e.g. $\tan ^{-1}(x)=\{\arctan(x)+\pi k\mid k\in \mathbb {Z} \}$ . However,

Revision as of 18:18, 25 January 2022 edit PCMorphy72 (talk \| contribs) Extended confirmed users 1,137 edits No edit summary ← Previous edit		Revision as of 18:56, 25 January 2022 edit undo PCMorphy72 (talk \| contribs) Extended confirmed users 1,137 edits Replaced a formula with a simpler one that also avoids a division by 0 / added an useful use of a notation Next edit →
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	<math display="block"> \operatorname{atan2}(y, x) = \lim_{z \to x^+}\arctan\left(\frac{y}{z}\right) + \frac{\pi}2\sgn(y)\sgn(x)\left(\sgn(x)-1\right) </math>		<math display="block"> \operatorname{atan2}(y, x) = \lim_{z \to x^+}\arctan\left(\frac{y}{z}\right) + \frac{\pi}2\sgn(y)\sgn(x)\left(\sgn(x)-1\right) </math>

	It ~~may~~ be useful ~~to use them~~ to define the [[Multivalued_function\|multivalued]] version of each inverse trigonometric function: e.g. ~~{{math\|tan<sup>−1</sup>(''x'')}}~~ <math>\tan^{-1}(x) = \{\~~operatorname{~~arctan(x) + 2\pi k \mid k \in \mathbb Z\}.</math>. However,		, that is useful e.g. to define the [[Multivalued_function\|multivalued]] version of each inverse trigonometric function: e.g. <math>\tan^{-1}(x) = \{\arctan(x) + \pi k \mid k \in \mathbb Z\}</math>. However,