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

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