Find the value of X in the equation COS(3X-180)=3/2

asked by guest
on Sep 21, 2024 at 2:22 am



You asked:

Solve the equation \[\cos\left( 3 X - 180 \right) = \frac{3}{2}\] for the unknown \(X\).

MathBot Answer:

There are no real solutions.

The complex solutions are: \[\begin{aligned}X &= \left\{60 - \frac{56 \pi}{3} + i \left(- \frac{\log{\left(7 - 3 \sqrt{5} \right)}}{6} + \frac{\log{\left(2 \right)}}{6}\right) + \frac{2 \pi n}{3}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{2.0943951 n + 1.3569372 + 0.32080788 i\; \middle|\; n \in \mathbb{Z}\right\}\\X &= \left\{60 - \frac{56 \pi}{3} + i \left(- \frac{\log{\left(7 + 3 \sqrt{5} \right)}}{6} + \frac{\log{\left(2 \right)}}{6}\right) + \frac{2 \pi n}{3}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{2.0943951 n + 1.3569372 - 0.32080788 i\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]

\(i\) is the imaginary unit, defined as \(i^2 = -1\).

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