24 = ((55)^2 sin 2x)/9.8
You asked:
Solve the equation \(24 = \frac{{55}^{2} \cdot \sin\left( 2 x \right)}{9.8}\) for the variable \(x\).
MathBot Answer:
The principal value in \(- \frac{\pi}{4} \le x \le \frac{\pi}{4}\) is \(x \approx 0.03891531\)
The real solutions are: \[\begin{aligned}x &= \left\{\frac{\arctan{\left(\frac{1176 \sqrt{227382649}}{227382649} \right)}}{2} + \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{3.1415927 n + 0.03891531\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{\pi}{2} - \frac{\arctan{\left(\frac{1176 \sqrt{227382649}}{227382649} \right)}}{2} + \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{3.1415927 n + 1.531881\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]