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calumus meretrix et gladio innocentis

### 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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### December 23, 2018

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