= Elliptic integral of the second kind
{title2=$E(k,\phi)=\int_0^\phi\sqrt{1-k^2\sin^2\theta}\,d\theta$}
For real modulus $0\leq k\leq1$, the displayed <integral> is the incomplete elliptic integral of the second kind, with amplitude $\phi$. The modulus convention matters: some sources instead use the parameter $m=k^2$. The <arc length> of an <ellipse> reduces to this <integral>, because a trigonometric parametrization gives a <square root> of $1-k^2\sin^2\theta$. At $k=0$ it reduces to $\phi$; at $k=1$ the real integrand is $|\cos\theta|$.
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