Difference between revisions of "Arcsin"

From specialfunctionswiki
Jump to: navigation, search
Line 36: Line 36:
  
 
=References=
 
=References=
*[http://mathworld.wolfram.com/InverseSine.html  Weisstein, Eric W. "Inverse Sine." From MathWorld--A Wolfram Web Resource.]
+
*[http://mathworld.wolfram.com/InverseSine.html  Weisstein, Eric W. "Inverse Sine." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/InverseSine.html]

Revision as of 01:34, 19 October 2014

The $\mathrm{arcsin}$ function is the inverse function of the sine function.
500px

Properties

Proposition: $$\dfrac{d}{dz} \mathrm{arcsin(z)} = \dfrac{1}{1-z^2}$$

Proof:

Proposition: $$\int \mathrm{arcsin}(z) dz = \sqrt{1-z^2}+z\mathrm{arcsin}(z)+C$$

Proof:

Proposition: $$\mathrm{arcsin}(z) = \mathrm{arccsc}\left( \dfrac{1}{z} \right)$$

Proof:

Proposition: $$\mathrm{arcsin}(z)=\sum_{k=0}^{\infty} \dfrac{\left(\frac{1}{2} \right)_n}{(2n+1)n!}x^{2n+1}$$

Proof:

References