My question: Regard the great circle $C$ that is created by the intersection of the sphere $x^2 +y^2 +z^2 =1$ and the plane $x+y+z=0$. Express the equations for the great circle $C$ in spherical coordinates.
Does anyone have an idea on how to solve this?
What I have done so far: Realized that $R=1$ for spherical coordinates, which gives: $\sin^2(x)\cos^2(v)+\sin^2(x)\sin^2(v)+\cos^2(v)=1$ for the first equation and $\sin x\cos v+\sin x\sin v+\cos v=0$ for the second equation. I don't know how to continue.