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Inverse trigonometric functions
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====Arctangent function with location parameter==== In many applications<ref>when a time varying angle crossing <math>\pm\pi/2</math> should be mapped by a smooth line instead of a saw toothed one (robotics, astronomy, angular movement in general){{citation needed|date=March 2020}}</ref> the solution <math>y</math> of the equation <math>x=\tan(y)</math> is to come as close as possible to a given value <math>-\infty < \eta < \infty</math>. The adequate solution is produced by the parameter modified arctangent function :<math> y = \arctan_\eta(x) := \arctan(x) + \pi \, \operatorname{rni}\left(\frac{\eta - \arctan(x)}{\pi} \right)\, . </math> The function <math>\operatorname{rni}</math> rounds to the nearest integer.
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