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The Derivative of Coversed Sine


Versed cosine, aka CVS, aka coversine

Do not confuse with versed cosign.

Contents

{$$ \operatorname{cvs}\theta = 1 - \sin\theta $$}

and perhaps with slightly more insight into the name:

{$$ \operatorname{cvs}\theta = \operatorname{ver} \left( {\pi \over 2} - \theta \right) $$}


{$ y = \operatorname{cvs}(x) $} and {$ y=\operatorname{arccvs}(x) $}

Demonstration:

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


''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 06, 2017

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