Difference between revisions of "Arccos"
From specialfunctionswiki
(→Properties) |
|||
| Line 9: | Line 9: | ||
<div class="mw-collapsible-content"> | <div class="mw-collapsible-content"> | ||
<strong>Proof:</strong> █ | <strong>Proof:</strong> █ | ||
| − | |||
</div> | </div> | ||
</div> | </div> | ||
| Line 20: | Line 19: | ||
</div> | </div> | ||
</div> | </div> | ||
| − | + | ||
<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> | <div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> | ||
| Line 27: | Line 26: | ||
<div class="mw-collapsible-content"> | <div class="mw-collapsible-content"> | ||
<strong>Proof:</strong> █ | <strong>Proof:</strong> █ | ||
| − | |||
</div> | </div> | ||
</div> | </div> | ||
Revision as of 01:29, 19 October 2014
The $\mathrm{arccos}$ function is the inverse function of the cosine function.
Properties
Proposition: $$\dfrac{d}{dz} \mathrm{arccos}(z) = -\dfrac{1}{\sqrt{1-z^2}}$$
Proof: █
Proposition: $$\int \mathrm{arccos}(z) dz = z\mathrm{arccos}(z)-\sqrt{1-z^2}+C$$
Proof: █
Proposition: $$\mathrm{arccos}(z)=\mathrm{arcsec} \left( \dfrac{1}{z} \right)$$
Proof: █
