Area of an elliptical arch Calculator

Calculates the area, length of chord and arch of elliptical arch given two semiaxes and two angles.

 angle θ0 degree radian angle θ1 same unit as θ0 semiaxis a semiaxis b 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt area of arch S length of chord c length of arch L
 $\normal Elliptical\ Arch\\(1)\ area:\\\hspace{20} S=F(\theta_1)-F(\theta_0)-{\large\frac{r_0 r_1}{2}}sin(\theta_1-\theta_0)\\\hspace{20} F(\theta)= {\large\frac{ab}{2}}\left[\theta-tan^{\small-1}\left({\large\frac{(b-a)sin2\theta}{b+a+(b-a)cos2\theta}}\right)\right]\\\hspace{20} r(\theta)^2={\large\frac{a^2b^2}{b^2cos^2\theta+a^2sin^2\theta}}\\\vspace{5}(2)\ elliptical\ arch :\\\hspace{20} L=aE({\large\frac{x(\theta_0)}{a}},k)-aE({\large\frac{x(\theta_1)}{a}},k)\\\hspace{20} x(\theta)=r(\theta)cos\theta,\ k=\sqrt{1-({\large\frac{b}{a}})^2}, \hspace{20} a\ge b,\hspace{10}\frac{\pi}{2}\ge \theta\ge 0\\\hspace{20} E(x,k):\ 2nd\ incomplete\ elliptic\ integral\\\vspace{5}(3)\ elliptical\ chord :\\\hspace{20} c=\sqrt{r(\theta_0)^2+r(\theta_1)^2-2r(\theta_0)r(\theta_1)cos(\theta_1-\theta_0)}\\$

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