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The Derivative of Versed Cosine


Versed cosine aka vercosin

Do not confuse with coversedsine.

Contents

{$$ \operatorname{vercosin}\theta = 1 + \cos\theta $$}

It is sometimes given as {$$ \operatorname{vercosin}\theta = 2\cos\left( {\theta \over 2} \right) $$}

For what it is worth, obviously:

{$$ \operatorname{vercosin}\theta = 2\cos\theta + \operatorname{ver}\theta $$}


{$ y = \operatorname{vercosin}(x) $} and {$ y=\operatorname{arcvercosin}(x) $}

The demonstration:

{$$ \begin{align} \operatorname{vercosin}\theta &= 1 + \cos\theta \cr (\operatorname{vercosin}\theta)^\prime &= (1 + \cos\theta)^\prime \cr &= (1)^\prime + \cos^\prime\theta \cr \therefore \quad \operatorname{vercosin}^\prime\theta &= - \sin\theta \end{align} $$}


Sources:

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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