solve, sin3x+cos3x=1/2
You asked:
Solve the equation \(\sin\left( 3 x \right) + \cos\left( 3 x \right) = \frac{1}{2}\) for the variable \(x\).
MathBot Answer:
The real solutions are: \[\begin{aligned}x &= \left\{- \frac{\arctan{\left(\frac{4}{3} - \frac{\sqrt{7}}{3} \right)}}{3} + \frac{2 \pi}{3} + \frac{2 \pi n}{3}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{2.0943951 n + 1.9530514\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{- \frac{\arctan{\left(\frac{4}{3} + \frac{\sqrt{7}}{3} \right)}}{3} + \frac{\pi}{3} + \frac{2 \pi n}{3}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{2.0943951 n + 0.66494245\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]