tan3x = -2
You asked:
Solve the equation \(\tan\left( 3 x \right) = -2\) for the variable \(x\).
MathBot Answer:
The principal value in \(- \frac{\pi}{6} < x < \frac{\pi}{6}\) is \(x \approx -0.36904957\)
The real solutions are: \[\begin{aligned}x &= \left\{- \frac{\arctan{\left(2 \right)}}{3} + \frac{\pi}{3} + \frac{2 \pi n}{3}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{2.0943951 n + 0.67814798\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{- \frac{\arctan{\left(2 \right)}}{3} + \frac{2 \pi}{3} + \frac{2 \pi n}{3}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{2.0943951 n + 1.7253455\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]