Arctangent formulas

\[ \textnormal{arctan}(-x) = -\textnormal{arctan}(x) \]

\[ \textnormal{sin}(\textnormal{arctan}(x)) = \dfrac{x}{\sqrt{1 + x^2}} \]

\[ \textnormal{cos}(\textnormal{arctan}(x)) = \dfrac{1}{\sqrt{1 + x^2}} \]

\[ \textnormal{tan}(\textnormal{arctan}(x)) = x \]

\[ \textnormal{arctan}\left(\dfrac{1}{x}\right) = \left\{ \begin{aligned} & \dfrac{\pi}{2} - \textnormal{arctan}(x) && (x>0) \\~\\ & -\dfrac{\pi}{2} - \textnormal{arctan}(x) && (x<0) \end{aligned} \right. \]

Trigonometry formula

Formula