Is $f(t)=(\cos(t),\sin(t))$ a function? In the Linear Algebra book we're using (Linear Algebra with Applications, Bretscher, p.129), the author defines this as the function of the unit circle.
I understand why the equation of a circle can't be a function. In this case however, I could see how despite failing the vertical line test, $f(t)=(\cos(t),\sin(t))$ still outputs a unique value for any $t$ and is therefore technically a function.
Is that the rationale, or is $f(t)=(\cos(t),\sin(t))$ not really a function despite what the author states?

This is just parametric equation of a circle $f(t)=\left[\begin{matrix}\cos t\\\sin t\end{matrix}\right]$ http://www.mathopenref.com/coordparamcircle.html, it's a function from $\mathbb{R}$ to $\mathbb{R}^2$ and its range is the unit circle centered at the origin.
