I have been trying to parametrise the curve $C$: Consider the cylinder $S$ given by the equation $x^2+y^2=1$ and the curve $C$ that is given by the intersection between the cylinder and the plane given by the equation $x + y = 0$
So, I can immediately put that $x=\cos t$ and $y=\sin t$. But how can I use the equation of the plane here? Should I put that then, according to the equation of the plane: $\cos t=-\sin t$ and hence $C: r(t)= -\sin t i+\sin t j+0k$?
Thanks