sin(2x)= -0.3

asked by guest
on Mar 29, 2025 at 2:57 am



You asked:

Solve the equation sin(2x)=0.3\sin\left( 2 x \right) = -0.3 for the variable xx.

MathBot Answer:

The principal value in π4xπ4- \frac{\pi}{4} \le x \le \frac{\pi}{4} is x0.15234633x \approx -0.15234633


The real solutions are: x={πarctan(39191)2+πn  |  nZ}{3.1415927n+2.9892463  |  nZ}x={π2+arctan(39191)2+πn  |  nZ}{3.1415927n+1.7231427  |  nZ}\begin{aligned}x &= \left\{\pi - \frac{\arctan{\left(\frac{3 \sqrt{91}}{91} \right)}}{2} + \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{3.1415927 n + 2.9892463\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{\pi}{2} + \frac{\arctan{\left(\frac{3 \sqrt{91}}{91} \right)}}{2} + \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{3.1415927 n + 1.7231427\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}