Difference between revisions of "Cotangent"
From specialfunctionswiki
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File:Complex Cot.jpg|[[Domain coloring]] of [[analytic continuation]] of $\cot$. | File:Complex Cot.jpg|[[Domain coloring]] of [[analytic continuation]] of $\cot$. | ||
</gallery> | </gallery> | ||
| + | </div> | ||
| + | |||
| + | =Properties= | ||
| + | <div class="toccolours mw-collapsible mw-collapsed"> | ||
| + | <strong>[[Derivative of cotangent|Proposition]]:</strong> $\dfrac{d}{dx}$[[Cotangent|$\cot$]]$(x)=-$[[Cosecant|$\csc$]]$^2(x)$ | ||
| + | <div class="mw-collapsible-content"> | ||
| + | <strong>Proof:</strong> █ | ||
| + | </div> | ||
</div> | </div> | ||
<center>{{:Trigonometric functions footer}}</center> | <center>{{:Trigonometric functions footer}}</center> | ||
Revision as of 05:22, 20 March 2015
The cotangent function is defined by the formula $$\cot(z)=\dfrac{1}{\tan z}=\dfrac{\cos(z)}{\sin(z)},$$ where $\tan$ denotes the tangent function.
- Cotangent.png
Plot of cotangent function on $\mathbb{R}$.
- Complex Cot.jpg
Domain coloring of analytic continuation of $\cot$.
Properties
Proposition: $\dfrac{d}{dx}$$\cot$$(x)=-$$\csc$$^2(x)$
Proof: █
