# The ring of real trigonometric polynomials

Desvl at
The ringThroughout we consider the polynomial ring $R=\mathbb{R}[\cos{x},\sin{x}].$ This ring has a lot of non-trivial properties which give us a good chance to study commutative ring theory.First of all, note it is immediate that $R \cong \mathbb{R}[X,Y]/(X^2+Y^2-1)$ if the map is given by \(X ……