Pregunta: 6. Show that x(u,v)=(usinαcosv,usinαsinv,ucosα)0

6. Show that $\begin{array}{l}\mathbf{x}(u,v)=(u\sin \alpha \cos v,u\sin \alpha \sin v,u\cos \alpha )\\ 0<u<\infty ,0<v<2\pi ,\alpha =\text{ const., }\end{array}$ is a parametrization of the cone with $2\alpha$ as the angle of the vertex. In the corresponding coordinate neighborhood, prove that the curve $\mathbf{x}(c\exp (v\sin \alpha \mathrm{cotan}\beta ),v),c=\text{ const., }\beta =\text{ const. },$ intersects the generators of the cone $(v=$ const.) under the constant angle $\beta$.