Question

using basic trigonometry derive the following equations, which are used to convert cartesian to polar coordinates and vice versa. why is the cos(phi)in the x term?

x = R cos (phi) sin (lamda)
y = R sin (phi)

they are used in orthogonal projection of a spherical surface to a flat surface in the (x y) plane.

where (phi)=latitude
(lamda)=longitude

Answer 1

wikipedia has a nice article explaining this projection. Your example uses an origin of (0,0) for the projection, reducing the complexity of the equations considerably.

Answer 2

Graph the oriented angle in standard position.
7π
4