Notes: `F(theta) = arcsin(sqrt(sin(theta)))` Find the derivative of the function. Simplify where possible.

$\displaystyle\frac{{d}}{{{\left.{d}{x}\right.}}}{{\sin}}^{{-{{1}}}}{\left({x}\right)}=\frac{{1}}{\sqrt{{{1}-{{x}}^{{2}}}}}$

$\displaystyle{F}{\left(\theta\right)}={{\sin}}^{{-{{1}}}}{\left(\sqrt{{{\sin{{\left(\theta\right)}}}}}\right)}$

$\displaystyle{F}'{\left(\theta\right)}={\left(\frac{{1}}{\sqrt{{{1}-{\sin{\theta}}}}}\right)}$
* d/(d theta)sqrt(sintheta)

$\displaystyle{F}'{\left(\theta\right)}={\left(\frac{{1}}{\sqrt{{{1}-{\sin{\theta}}}}}\right)}$
*(1/2)(sintheta)^(-1/2) costheta

$\displaystyle{F}'{\left(\theta\right)}=\frac{{\cos{\theta}}}{{{\left({2}\sqrt{{{\sin{\theta}}}}\sqrt{{{1}-{\sin{\theta}}}}\right)}}}$

Notes