Difference between revisions of "Arcsin"
From specialfunctionswiki
| Line 1: | Line 1: | ||
__NOTOC__ | __NOTOC__ | ||
The function $\mathrm{arcsin} \colon \mathbb{C} \setminus \left\{ (-\infty,-1) \bigcup (1,\infty) \right\} \rightarrow \mathbb{C}$ is defined by | The function $\mathrm{arcsin} \colon \mathbb{C} \setminus \left\{ (-\infty,-1) \bigcup (1,\infty) \right\} \rightarrow \mathbb{C}$ is defined by | ||
| − | $$\rm{arcsin}=-i \log \left( iz + \sqrt{1-z^2} \right),$$ | + | $$\rm{arcsin}(z)=-i \log \left( iz + \sqrt{1-z^2} \right),$$ |
where $i$ denotes the [[imaginary number]] and $\log$ denotes the [[logarithm]]. <br /> | where $i$ denotes the [[imaginary number]] and $\log$ denotes the [[logarithm]]. <br /> | ||
Revision as of 19:56, 22 November 2016
The function $\mathrm{arcsin} \colon \mathbb{C} \setminus \left\{ (-\infty,-1) \bigcup (1,\infty) \right\} \rightarrow \mathbb{C}$ is defined by
$$\rm{arcsin}(z)=-i \log \left( iz + \sqrt{1-z^2} \right),$$
where $i$ denotes the imaginary number and $\log$ denotes the logarithm.
Graph of $\mathrm{arcsin}$ on $[-1,1]$.
Domain coloring of $\mathrm{arcsin}$.
Properties
Derivative of arcsin
Antiderivative of arcsin
Relationship between arcsin and arccsc
2F1(1/2,1/2;3/2;z^2)=arcsin(z)/z
Videos
Inverse Trig Functions: Arcsin
Integrate x*arcsin(x)
What is arcsin(x)?
What is the inverse of arcsin(ln(x))?
See Also
References
On the function arc sin(x+iy)-Cayley
