sin x = 5/13
You asked:
Solve the equation \(\sin\left( x \right) = \frac{5}{13}\) for the variable \(x\).
MathBot Answer:
The principal value in \(- \frac{\pi}{2} \le x \le \frac{\pi}{2}\) is \(x \approx 0.39479112\)
The real solutions are: \[\begin{aligned}x &= \left\{2 \pi n + \arctan{\left(\frac{5}{12} \right)}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 0.39479112\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\pi - \arctan{\left(\frac{5}{12} \right)} + 2 \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 2.7468015\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]