The latitude and longitude of a point P in the Northern Hemisphere are related to spherical coordinate (ρ, θ, ø) as follows. We take the origin to be the center of the earth and the positive z-axis to pass through the North Pole. The positive x-axis passes through the point where the prime meridian (the meridian through Greenwich, England) intersects the equator. Then the latitude of P is α = 90° -ø° and the longitude is β = 360° - ø°. To the nearest mile, find the great circle distance from Los Angeles (lat. 34.06°N, long. 118.25°W) to San Francisco (lat. 37.71°N, long. 122.28°W). Take the radius of the earth to be 3960 mi. (A great circle is the circle of intersection of a sphere and a plane through the center of the sphere.)