Question

An xyz-coordinate system is placed with its origin at the center of the earth, so that
the equator (consisting of points with 0-degree latitude) is in the xy-plane, the North Pole
(the only point with 90-degree latitude) has coordinates (0, 0, 3960), and the prime meridian
(see the next paragraph) is in the xz-plane. Where the prime meridian crosses the equator,
the positive x-axis emerges from the South Atlantic Ocean, near the coast of Ghana.
The prime meridian is the great semicircle that runs through Greenwich, England on its way
from the North Pole to the South Pole. Points on this meridian are all said to have longitude
0 degrees. The point (0, 3960, 0) has longitude 90 degrees east, and the point (0, −3960, 0)
has longitude 90 degrees west. Thus the positive y-axis points east, into the Indian Ocean.
(a)Make a large diagram of this coordinate system.
(b)The latitude of Greenwich is 51 degrees north. What are its xyz-coordinates?

(c)There is a point on the equator whose longitude is 33 degrees east. What are its xyz-
coordinates?

(d)The latitude of Ankara, Turkey, is 40 degrees north. What is its z-coordinate? The
longitude of Ankara is 33 degrees east. What are its xy-coordinates?

I just need an explanation for 296 d thx

Answer 1

clearly, the radius r = 3960
x^2 + y^2 = r^2
for latitude θ, z = rsinθ
for longitude Ø, (x,y,z) = (rcosθcosØ,rcosθsinØ,rsinθ)