cos(x) + 2sin(x) =1.5
You asked:
Solve the equation \(\cos\left( x \right) + 2 \cdot \sin\left( x \right) = 1.5\) for the variable \(x\).
MathBot Answer:
The real solutions are: \[\begin{aligned}x &= \left\{- \arctan{\left(\frac{8}{7} - \frac{3 \sqrt{11}}{7} \right)} + 2 \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 0.27166684\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\pi - \arctan{\left(\frac{8}{7} + \frac{3 \sqrt{11}}{7} \right)} + 2 \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 1.9426306\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]