solve for c, cosh(c) = 2
You asked:
Solve the equation \[\cosh\left( c \right) = 2\] for the unknown \(c\).
MathBot Answer:
The real solutions are: \[\begin{aligned}c &= \log{\left(2 + \sqrt{3} \right)} \approx 1.3169579\\c &= \log{\left(2 - \sqrt{3} \right)} \approx -1.3169579\end{aligned}\]
The complex solutions are: \[\begin{aligned}c &= \left\{2 \pi i n + \log{\left(2 + \sqrt{3} \right)}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n i + 1.3169579\; \middle|\; n \in \mathbb{Z}\right\}\\c &= \left\{2 \pi i n + \log{\left(2 - \sqrt{3} \right)}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n i - 1.3169579\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]
\(i\) is the imaginary unit, defined as \(i^2 = -1\).
asked 2 days ago
active 2 days ago