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...    

$\cos2\pi/7$ is a root of a cubic equation with integer coefficients. You can find that cubic by using $\cos\theta=(1/2)(e^{i\theta}+e^{-i\theta})$, computing the square and the cube, and looking for linear relations, bearing in mind that the $7$ $7$th roots of unity add up to zero. Then you can use Cardano's formula to solve the cubic. I don't know if I recommend actually doing all this - I'm sure you get a mess, although the discriminant will be a perfect square, so you'll get some simplification there. 
