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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> |
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, 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, this might appear to conflict logically with the common semantics for expressions such as {{math|sin<sup>2</sup>(''x'')}} (although |
, 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, this might appear to conflict logically with the common semantics for expressions such as {{math|sin<sup>2</sup>(''x'')}} (although only {{math|sin<sup>2</sup> ''x''}}, without brackets, is really common one) |
Revision as of 19:24, 25 January 2022
Formula without apparent conditional construct:
, that is useful e.g. to define the multivalued version of each inverse trigonometric function: e.g. . However, this might appear to conflict logically with the common semantics for expressions such as sin2(x) (although only sin2 x, without brackets, is really common one)