Trigonometric functions of 
for 
prime have an especially complicated Galois-minimal representation.
In particular, the case 
requires approximately 500 MB of space using the
Wolfram Language command Developer`TrigToRadicals[Cos[Pi/23]].
However, they can be expressed concisely as algebraic numbers. For example, letting
denote the 
th
root of the polynomial 
using the ordering of the Wolfram
Language's Root
function, 
is given by
 |
and 
by
 |
