2sinx-3cosx=1
You asked:
Solve the equation \(2 \sin\left( x \right) - 3 \cos\left( x \right) = 1\) for the variable \(x\).
MathBot Answer:
The real solutions are: \[\begin{aligned}x &= \left\{2 \pi n + \arctan{\left(2 + \frac{2 \sqrt{3}}{3} \right)}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 1.2638286\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\pi + 2 \pi n + \arctan{\left(2 - \frac{2 \sqrt{3}}{3} \right)}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 3.8433515\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]