cosec2x=5

asked by guest
on Nov 23, 2024 at 7:55 am



You asked:

Solve the equation \(\csc\left( 2 x \right) = 5\) for the variable \(x\).

MathBot Answer:

The principal value in \(x > - \frac{\pi}{4} \wedge x < \frac{\pi}{4} \wedge x \neq 0\) is \(x \approx 0.10067896\)

The real solutions are: \[\begin{aligned}x &= \left\{\frac{\arctan{\left(\frac{\sqrt{6}}{12} \right)}}{2} + \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{3.1415927 n + 0.10067896\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{\pi}{2} - \frac{\arctan{\left(\frac{\sqrt{6}}{12} \right)}}{2} + \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{3.1415927 n + 1.4701174\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]

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