I am terrible at proofs and trig-so this is like a double whammy, and i have tried these ones for hours to no avail

1. Prove that sin 1/6pi=1/2 , cos 1/6pi=1/2 sq.rt.(3)

...it says hint: use previous example, which asks to prove sin3x=3sinx-4sin^3 x and cos3x=cosx -4sin^2 x cosx....prove also cos3x=4cos^3 x -3cosx

(im not too worried about the hint part---just posted it incase someone found it helpful while prooving)

2. prove that sin 1/3pi=1/2sq.rt. 3, cos 1/3pi=1/2

3. prove that sine 1/4pi=cos 1/4pi=1/2 sq.rt. 2

any explanations and help is greatly apprecaited....thanks in advance