Is there a way to solve $ax + \sin(bx+c) = d$ analytically for x? Here a, b, c and d are constants.
2026-03-27 07:13:18.1774595598
Is there a way to solve $ax + \sin(bx+c) = d$ analytically?
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There is no closed form in terms of any generally-accepted mathematical functions, as far as I am aware. In particular, the fixed point of the cosine function, i.e. the sole real solution of
$$\cos(x) = x$$
which is equivalent to
$$\sin\left(\frac{\pi}{2} - x\right) = x$$
is famously non-explicit. Hence, there can be no explicit formula for general values of $a$, $b$, $c$, and $d$ for the solutions of the equation you give.