solve 4sin^2(x)+3sinxcosx=2
You asked:
Solve the equation \(4 \cdot {\sin\left( x \right)}^{2} + 3 \cdot \sin\left( x \right) \cdot \cos\left( x \right) = 2\) for the variable \(x\).
MathBot Answer:
The real solutions are: \[\begin{aligned}x &= \left\{\frac{\arctan{\left(\frac{4}{3} \right)}}{2} + \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{3.1415927 n + 0.46364761\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{\pi}{2} + \frac{\arctan{\left(\frac{4}{3} \right)}}{2} + \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{3.1415927 n + 2.0344439\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]