Find a: cos(.034849a) = -0.870398
You asked:
Solve the equation \[\cos\left( .034849 a \right) = -0.870398\] for the unknown \(a\).
MathBot Answer:
The principal value in \(0 \le a \le \frac{1000000 \pi}{34849}\) is \(a \approx 75.37681\)
The real solutions are: \[\begin{aligned}a &= \left\{\frac{1000000 \pi}{34849} + \frac{1000000 \arctan{\left(\frac{3 \sqrt{6733536711}}{435199} \right)}}{34849} + \frac{2000000 \pi n}{34849}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{180.29743 n + 104.92063\; \middle|\; n \in \mathbb{Z}\right\}\\a &= \left\{- \frac{1000000 \arctan{\left(\frac{3 \sqrt{6733536711}}{435199} \right)}}{34849} + \frac{1000000 \pi}{34849} + \frac{2000000 \pi n}{34849}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{180.29743 n + 75.37681\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]