Explanation Assume that a point A ( cos α , sin α ) subtended at angle α moves toward a point B ( cos β , sin β ) subtended at angle β in a rectangular coordinate system . The shortest distance between points A and B by using the distance formula is A B = ( cos α − c o s β ) 2 + ( sin α − sin β ) 2 = cos 2 α + cos 2 β − 2 cos α cos β + s i n 2 α + s i n 2 β − 2 s i n α s i n β = ( cos 2 α + s i n 2 α ) + ( cos 2 β + s i n 2 β ) − 2 ( cos α cos β + s i n α s i n β ) = 1 +

16th Edition

ISBN: 9781323142707

Author: Blitzer

Publisher: Pearson Custom Publishing

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System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

Chapter 6.2, Problem 87E

To determine

The distance formula and definitions of cosine and sine are used to prove the formula for cosine of the difference of two angles.

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Chapter 6.2, Problem 86E

Chapter 6.2, Problem 88E

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