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Unformatted text preview: Let a, b, c be the radian measures of the sides of a spherical triangle. Let C be the angle of the triangle opposite side c , i.e., between sides α and β , which means that C is the angle between the tangent vectors to the two arcs of great circles meeting at that vertex. (a) (10 pts.) Prove the spherical law of cosines , which says that cos c = cos a cos b + sin a sin b cos C. (b) (7 pts.) What does this relation say approximately when a, b, c are very small? (Expand the functions of a, b, c in power series, and approximate by discarding any term involving a product of three or more factors a, b, c , such as b 2 c .) Reminder: Please write “Sources consulted: none” at the top of your homework, or list your (animate and inanimate) sources. See the course information sheet for details. 1...
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This note was uploaded on 09/14/2011 for the course MATH 18.02 taught by Professor Auroux during the Fall '08 term at MIT.
- Fall '08
- Multivariable Calculus