sin2theta=0.5

asked by guest
on Jan 15, 2025 at 7:54 am



You asked:

Solve the equation \(\sin\left( 2 θ \right) = 0.5\) for the variable \(θ\).

MathBot Answer:

The principal value in \(- \frac{\pi}{4} \le θ \le \frac{\pi}{4}\) is \(θ \approx 0.26179939\)


The real solutions are: \[\begin{aligned}θ &= \left\{\pi \left(\frac{1}{12} + n\right)\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{3.1415927 n + 0.26179939\; \middle|\; n \in \mathbb{Z}\right\}\\θ &= \left\{\frac{\pi \left(5 + 12 n\right)}{12}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{3.1415927 n + 1.3089969\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]