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calumus meretrix et gladio innocentis

The Derivative of Coversed Cosine


Do not confuse with versed cosine.

Contents

{$$ \begin{align} \operatorname{covercosin}\theta &= 1 + \sin\theta \cr &= \operatorname{vercosin}\left( {\pi \over 2} - \theta \right) \end{align} $$}

I have not yet found a good geometric representation of this function in relation to the basic trig functions.


{$ y=\operatorname{covercosin}(x) $} and {$ y=\operatorname{arccovercosin}(x) $}

{$$ \begin{align} \operatorname{covercosin}\theta &= 1 + \sin\theta \cr {d \over {d\theta}}\operatorname{covercosin}\theta &= {d \over {d\theta}}\left( 1 + \sin\theta \right) \cr &= {d \over {d\theta}}1 + {d \over {d\theta}}\sin\theta \cr &= 0 + \cos\theta \cr \therefore \quad {d \over {d\theta}}\operatorname{covercosin}\theta &= \cos\theta \end{align} $$}


''Sources:'

  1. FooPlot: Online graphing calculator and function plotter

Recommended:

Category: Math Calculus Trigonometry


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This is a student's notebook. I am not responsible if you copy it for homework, and it turns out to be wrong.

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August 08, 2017

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