Anybody can solve this equation for me? $$\sin(x) + \sin(2x) + \sin(3x) - \sqrt 3 = 0.$$ I imported it to my cas calculator and this was the output: $$\left\{x = 2k π + (1/3) π, x = 2k π + 0.3202568022849\right\}$$ The problem is I don't know were the $0.3202568022849$ is coming from and it should not be as constant number I have to write it as mathematical form.
2026-03-29 09:10:12.1774775412
Solving the trigonometric equation $\sin(x) + \sin(2x) + \sin(3x) - \sqrt 3 = 0$
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There are two ways you could do it...
Use the sum-to-product formulas (preferably one that makes the angles simple), factor, and then determine which root is correct.
Expand $\sin 2x$ and $\sin 3x$, group like terms, and then determine which root is correct.