Exact values of $\cos(2\pi/7)$ and $\sin(2\pi/7)$ What are the exact values of $\cos(2\pi/7)$ and $\sin(2\pi/7)$ and how do I work it out?
I know that $\cos(2\pi/7)$ and $\sin(2\pi/7)$ are the real and imaginary parts of $e^{2\pi i/7}$ but I am not sure if that helps me...    

There is a little problem if you want to express $\cos(2\pi/7)$ in terms of radicals. As Gerry Myerson wrote, it is a root of a degree $3$ polynomial ($e^{2\pi i /7}$ is a root of $x^6+x^5+\dots+1=0$, $\cos(2\pi/7)=y=(x+x^{-1})/2$, which gives $8 y^3+4 y^2-4 y-1 = 0$). That polynomial ($8 y^3+4 y^2-4 y-1$) is irreducible (over $\mathbb{Q}$) and has real roots (namely $\cos(2\pi/7),\cos(4\pi/7),\cos(6\pi/7)$). There is a famous theorem (casus irreducibilis) saying that the roots of the polynomial cannot be expressed using real radicals. So you will need complex numbers in your formula for $\cos(2\pi/7)$. 
(Cardano's formula gives
$$y= -1/6+7^{2/3}/(3\times 2^{2/3} (1+3 i \sqrt{3})^{1/3})+ (7/2\times (1+3 i \sqrt{3}))^{1/3}/6 $$
- computed by Wolfram Alpha) 
