Proving exp(2 pi i t) is a bijection onto unit circle

how would a prove that f (t)= exp ( 2 pi i t) with the equivalence relation f ~ f+1, is a bijection onto the unit circle S1 in the complex plane. i just dont know how to get started on proving this, I can see its quite obvious geometrically but dont know how to formalize this...

Can you show that $\displaystyle f:\left[ {0,2\pi } \right) \mapsto \left\{ {\left( {x,y} \right):x^2 + y^2 = 1} \right\}\,,\,f(t) = \left( {\cos (t),\sin (t)} \right)$ is a bijection?