Trigonometric functions of for an integer cannot be expressed in terms of sums, products, and finite root extractions on real rational numbers because 11 is not a Fermat Prime. This also means that the Undecagon is not a Constructible Polygon.
However, exact expressions involving roots of complex numbers can still be derived using the trigonometric identity
See also Undecagon
Beyer, W. H. ``Trigonometry.'' CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press,