Los Angeles is located at North latitude and West longitude, and Rio de Janeiro, Brazil

Chapter 11, Problem 16

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Los Angeles is located at North latitude and West longitude, and Rio de Janeiro, Brazil is located at South latitude and West longitude (see figure). Assume that Earth is spherical and has a radius of 4000 miles. (a) Find the spherical coordinates for the location of each city. (b) Find the rectangular coordinates for the location of each city. (c) Find the angle (in radians) between the vectors from the center of Earth to each city. (d) Find the great-circle distance between the cities. Hint: (e) Repeat parts (a)(d) for the cities of Boston, located at North latitude and West longitude, and Honolulu, located at North latitude and West longitude.

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