solve 11^2=15^2+8^2-2(15)(8)cos(x)
You asked:
Solve the equation \({11}^{2} = {15}^{2} + {8}^{2} - 2 \cdot 15 \cdot 8 \cos\left( x \right)\) for the variable \(x\).
MathBot Answer:
The principal value in \(0 \le x \le \pi\) is \(x \approx 0.79539883\)
The real solutions are: \[\begin{aligned}x &= \left\{2 \pi n + \arctan{\left(\frac{\sqrt{51}}{7} \right)}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 0.79539883\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{- \arctan{\left(\frac{\sqrt{51}}{7} \right)} + 2 \pi + 2 \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 5.4877865\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]