# Area of an elliptical sector Calculator

## Calculates the area and arc of an elliptical sector given two axes and two angles.

 angle θ0 degree radian angle θ1 same unit as θ0 semimajor axis a semiminor axis b 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt area of sector S length of arc L
 $\normal Elliptical\ Sector\\(1)\ area:\\\hspace{20} S=F(\theta_1)-F(\theta_0)\\\hspace{20} F(\theta)= {\large\frac{ab}{2}}\left[\theta-tan^{\small-1}\left({\large\frac{(b-a)sin2\theta}{b+a+(b-a)cos2\theta}}\right)\right]\\\hspace{20} r(\theta)^2={\large\frac{a^2b^2}{b^2cos^2\theta+a^2sin^2\theta}}\\\vspace{5}(2)\ elliptical\ arch :\\\hspace{20} L=aE({\large\frac{x(\theta_0)}{a}},k)-aE({\large\frac{x(\theta_1)}{a}},k)\\\hspace{20} x(\theta)=r(\theta)cos\theta,\ k=\sqrt{1-({\large\frac{b}{a}})^2},\hspace{20} a\ge b,\hspace{10}\frac{\pi}{2}\ge \theta\ge 0\\\hspace{20} E(x,k):\ 2nd\ incomplete\ elliptic\ integral\\$

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