Difference between revisions of "Arctan"
From specialfunctionswiki
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| + | [http://mathworld.wolfram.com/InverseTangent.html Weisstein, Eric W. "Inverse Tangent." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/InverseTangent.html] | ||
Revision as of 01:33, 19 October 2014
The $\mathrm{arctan}$ function is the inverse function of the tangent function.
Properties
Proposition: $$\dfrac{d}{dz} \mathrm{arctan}(z) = \dfrac{1}{z^2+1}$$
Proof: █
Proposition: $$\int \mathrm{arctan}(z) = z\mathrm{arctan}(z) - \dfrac{1}{2}\log(1+z^2)+C$$
Proof: █
Proposition: $$\mathrm{arctan}(z) = \mathrm{arccot}\left( \dfrac{1}{z} \right)$$
Proof: █
