-11=25\cos 40+60\cos \theta -80\cos 50
You asked:
Solve the equation \(-11 = 25 \cdot \cos\left( 40 \right) + 60 \cdot \cos\left( θ \right) - 80 \cdot \cos\left( 50 \right)\) for the variable \(θ\).
MathBot Answer:
The 2 solutions to the equation are: \[\begin{aligned}θ &= \operatorname{im}{\left(\arccos{\left(- \frac{11}{60} - \frac{5 \cos{\left(40 \right)}}{12} + \frac{4 \cos{\left(50 \right)}}{3} \right)}\right)} i \approx 0.84753566 i\\θ &= 2 \pi - \arccos{\left(- \frac{11}{60} - \frac{5 \cos{\left(40 \right)}}{12} + \frac{4 \cos{\left(50 \right)}}{3} \right)} \approx 6.2831853 -0.84753566 i\end{aligned}\]