2+5cos(3x)=4
You asked:
Solve the equation \(2 + 5 \cos\left( 3 x \right) = 4\) for the variable \(x\).
MathBot Answer:
The principal value in \(0 \le x \le \frac{\pi}{3}\) is \(x \approx 0.38642649\)
The real solutions are: \[\begin{aligned}x &= \left\{\frac{\arctan{\left(\frac{\sqrt{21}}{2} \right)}}{3} + \frac{2 \pi n}{3}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{2.0943951 n + 0.38642649\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{- \frac{\arctan{\left(\frac{\sqrt{21}}{2} \right)}}{3} + \frac{2 \pi}{3} + \frac{2 \pi n}{3}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{2.0943951 n + 1.7079686\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]