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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

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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