Difference between revisions of "Arcsin"
From specialfunctionswiki
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The $\mathrm{arcsin}$ function is the inverse function of the [[sine]] function. <br /> | The $\mathrm{arcsin}$ function is the inverse function of the [[sine]] function. <br /> | ||
[[File:Arcsin.png|500px]] | [[File:Arcsin.png|500px]] | ||
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| + | [[File:Complex arcsin.jpg|500px]] | ||
=Properties= | =Properties= | ||
Revision as of 04:55, 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: █
