For a constant, N
, what value of x
will maximize the cosine (or any trig) function?
\begin{equation} 1 = \cos{(Nx)} \end{equation}
I am looking for the exact form, not the approximation because, \begin{equation} \frac{\arccos{(1)}}{N} = x = 0 \end{equation}
For example, WolframAlpha.com states that if N = 19.013
, then,
\begin{equation}
x = \frac{2000 \pi n}{19013} , n \text{ } \varepsilon \text{ } \text{set of integers}
\end{equation}
How was that solution calculated?