cos2x=-1/2
You asked:
Solve the equation \(\cos\left( 2 x \right) = \frac{-1}{2}\) for the variable \(x\).
MathBot Answer:
The principal value in \(0 \le x \le \frac{\pi}{2}\) is \(x \approx 1.0471976\)
The real solutions are: \[\begin{aligned}x &= \left\{\pi \left(\frac{1}{3} + n\right)\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{3.1415927 n + 1.0471976\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{\pi \left(2 + 3 n\right)}{3}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{3.1415927 n + 2.0943951\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]