I am just starting to learn mathematics though self study and I am curious about the following:
Define $S=\{(x_1,x_2)\in\mathbb{R^2}:x_1^2+x_2^2=1\}$. How can I show (directly from the definition) that the map $f:\mathbb{R}\to S$ where $f(t)=\big(\cos(2\pi t), \sin(2\pi t)\big)$ is surjective?
Thank you in advance.