sin2θ=0.125
find θ
You asked:
Solve the equation \[\sin\left( 2 θ \right) = 0.125\] for the unknown \(θ\).
MathBot Answer:
The principal value in \(- \frac{\pi}{4} \le θ \le \frac{\pi}{4}\) is \(θ \approx 0.062663916\)
The real solutions are: \[\begin{aligned}θ &= \left\{\frac{\arctan{\left(\frac{\sqrt{7}}{21} \right)}}{2} + \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{3.1415927 n + 0.062663916\; \middle|\; n \in \mathbb{Z}\right\}\\θ &= \left\{\frac{\pi}{2} - \frac{\arctan{\left(\frac{\sqrt{7}}{21} \right)}}{2} + \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{3.1415927 n + 1.5081324\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]