Susan Hallstrom, Numerade Educator

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Calculus: Early Transcendentals

The latitude and longitude of a point $ P $ in the Northern Hemisphere are related to spherical coordinates $ \rho, \theta, \phi $ 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 $ \alpha = 90^\circ - \phi^\circ $ and the longitude is $ \beta = 360^\circ - \theta^\circ $. Find the great-circle distance from Los Angeles (lat. $ 34.06^\circ N $, long. $ 118.25^\circ W $) to Montreal (lat. $ 45.50^\circ N $, long. $ 73.60^\circ 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.)

Chapter 15: Multiple Integrals

Section 8: Triple Integrals in Spherical Coordinates