I am having a problem solving the following equation. Please help.
$12(\cos(x))^3+2\cos(x)^2+(24\sin(x)-3)\cos(x)+2\sin(x)= 0$
Thank you in advance
I am having a problem solving the following equation. Please help.
$12(\cos(x))^3+2\cos(x)^2+(24\sin(x)-3)\cos(x)+2\sin(x)= 0$
Thank you in advance
$s = \sin(x)$ must satisfy the equation $144\,{s}^{6}-576\,{s}^{5}+220\,{s}^{4}+1000\,{s}^{3}-283\,{s}^{2}-424 \,s-77 = 0$. This has Galois group $S_6$, so it can't be solved in terms of radicals. Thus you aren't going to get nice closed-form solutions. The four solutions for $0 \le x \le 2 \pi$ are approximately $1.66661701719437, 3.42548142597468, 4.63849563287631, 5.91793801389173$ (found by numerical methods).