Difference between revisions of "Arccos"
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| − | The $\mathrm{arccos}$ | + | __NOTOC__ |
| + | The function $\mathrm{arccos} \colon \mathbb{C} \setminus \{(-\infty,-1) \bigcup (1,\infty) \} \rightarrow \mathbb{C}$ is defined by | ||
| + | $$\rm{arccos}(z)=\dfrac{\pi}{2} + i\log\left( iz + \sqrt{1-z^2} \right),$$ | ||
| + | where $i$ denotes the [[imaginary number]] and $\log$ denotes the [[logarithm]]. | ||
| − | [ | + | <div align="center"> |
| + | <gallery> | ||
| + | File:Arccosplot.png|Graph of $\mathrm{arccos}$ on $[-1,1]$. | ||
| + | File:Complexarccosplot.png|[[Domain coloring]] of $\mathrm{arccos}$. | ||
| + | </gallery> | ||
| + | </div> | ||
=Properties= | =Properties= | ||
| − | < | + | [[Arccos as inverse cosine]]<br /> |
| − | < | + | [[Derivative of arccos]]<br /> |
| − | + | [[Antiderivative of arccos]]<br /> | |
| − | + | ||
| − | + | =References= | |
| − | </ | + | [http://mathworld.wolfram.com/InverseCosine.html Weisstein, Eric W. "Inverse Cosine." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/InverseCosine.html] |
| − | </ | + | |
| + | =See Also= | ||
| + | [[Cosine]] <br /> | ||
| + | [[Cosh]] <br /> | ||
| + | [[Arccosh]] | ||
| − | + | {{:Inverse trigonometric functions footer}} | |
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| − | + | [[Category:SpecialFunction]] | |
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Latest revision as of 20:04, 22 November 2016
The function $\mathrm{arccos} \colon \mathbb{C} \setminus \{(-\infty,-1) \bigcup (1,\infty) \} \rightarrow \mathbb{C}$ is defined by $$\rm{arccos}(z)=\dfrac{\pi}{2} + i\log\left( iz + \sqrt{1-z^2} \right),$$ where $i$ denotes the imaginary number and $\log$ denotes the logarithm.
Graph of $\mathrm{arccos}$ on $[-1,1]$.
Domain coloring of $\mathrm{arccos}$.
Properties
Arccos as inverse cosine
Derivative of arccos
Antiderivative of arccos
