Difference between revisions of "Arcsec"

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[[File:Complex ArcSec.jpg|500px]]
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The [[function]] $\mathrm{arcsec} \colon \mathbb{R} \setminus (-1,1) \rightarrow [0,\pi] \setminus \left\{ \dfrac{\pi}{2} \right\}$ is the [[inverse function]] of the [[secant]] function.
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<gallery>
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File:Arcsecplot.png|Graph of $\mathrm{arcsec}$.
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File:Complexarcsecplot.png|[[Domain coloring]] of $\mathrm{arcsec}$.
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</gallery>
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</div>
  
 
=Properties=
 
=Properties=
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[[Derivative of arcsec]]
<strong>Proposition:</strong>  
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$$\dfrac{d}{dz} \mathrm{arcsec}(z) = -\dfrac{1}{\sqrt{z^2-1}|z|}$$
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=See Also=
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[[Secant]] <br />
<strong>Proof:</strong> █
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[[Sech]] <br />
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[[Arcsech]]
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{{:Inverse trigonometric functions footer}}
  
<center>{{:Inverse trigonometric functions footer}}</center>
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[[Category:SpecialFunction]]

Latest revision as of 03:44, 6 July 2016

The function $\mathrm{arcsec} \colon \mathbb{R} \setminus (-1,1) \rightarrow [0,\pi] \setminus \left\{ \dfrac{\pi}{2} \right\}$ is the inverse function of the secant function.

Properties

Derivative of arcsec

See Also

Secant
Sech
Arcsech

Inverse trigonometric functions