sin3x=1/4
You asked:
Solve the equation \(\sin\left( 3 x \right) = \frac{1}{4}\) for the variable \(x\).
MathBot Answer:
The principal value in \(- \frac{\pi}{6} \le x \le \frac{\pi}{6}\) is \(x \approx 0.084226752\)
The real solutions are: \[\begin{aligned}x &= \left\{\frac{\arctan{\left(\frac{\sqrt{15}}{15} \right)}}{3} + \frac{2 \pi n}{3}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{2.0943951 n + 0.084226752\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{- \frac{\arctan{\left(\frac{\sqrt{15}}{15} \right)}}{3} + \frac{\pi}{3} + \frac{2 \pi n}{3}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{2.0943951 n + 0.9629708\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]