4.22. Let's introduce a coordinate system with the origin $O$ at the center of the Earth, with the axes $O x$ and $O y$ passing through the points on the equator with longitudes $0^{\circ}$ and $90^{\circ}$ respectively, and the axis $\mathrm{Oz}$ passing through the North Pole. What are the coordinates of a point on the Earth's surface with latitude $\varphi$ and longitude $\psi$? (Consider the Earth as a sphere of radius $R$; in the southern hemisphere, the latitude is taken as negative.)