sin(8 times x)=0.817
You asked:
Solve the equation \(\sin\left( 8 x \right) = 0.817\) for the variable \(x\).
MathBot Answer:
The principal value in \(- \frac{\pi}{16} \le x \le \frac{\pi}{16}\) is \(x \approx 0.11952364\)
The real solutions are: \[\begin{aligned}x &= \left\{\frac{\arctan{\left(\frac{817 \sqrt{332511}}{332511} \right)}}{8} + \frac{\pi n}{4}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{0.78539816 n + 0.11952364\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{- \frac{\arctan{\left(\frac{817 \sqrt{332511}}{332511} \right)}}{8} + \frac{\pi}{8} + \frac{\pi n}{4}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{0.78539816 n + 0.27317544\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]