I need to solve the equation: $$k_0\sin^{-1}(\alpha x)+k_1\sqrt{(R^2-x^2)}=\Sigma$$ for the variable $x$. $(k_0,\alpha,k_1,R,\Sigma)$ are constants. I am not able to find close solutions for it. Is there some way to solve this equation avoiding numerical methods? Thanks.
2026-03-18 21:25:26.1773869126
Solutions of the equation $k_0\sin^{-1}(\alpha x)+k_1\sqrt{(R^2-x^2)}=\Sigma$
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