Explanation Given Information: Polar coordinates ( r 1 , θ 1 ) and ( r 2 , θ 2 ) Formula used: d = ( y 2 − y 1 ) 2 + ( x 2 − x 1 ) 2 Proof: The distance between two points in rectangular coordinates ( x 1 , y 1 ) and ( x 2 , y 2 ) is given by d = ( y 2 − y 1 ) 2 + ( x 2 − x 1 ) 2 Substitute x 1 = r 1 cos θ 1 , y 1 = r 1 sin θ 1 and x 2 = r 2 cos θ 2 , y 2 = r 2 sin θ 2 to get d = ( r 2 sin θ 2 − r 1 sin θ 1 ) 2 + ( r 2 cos θ 2 − r 1 sin θ 1 ) 2 = r 2 2 sin 2 θ 2 + r 1 2 sin 2 θ 1 −

Blitzer: Precalculus Essentials_5 (5th Edition)

5th Edition

ISBN: 9780134578156

Author: Robert F. Blitzer

Publisher: PEARSON

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Chapter 6.3, Problem 107PE

To determine

To prove: That the distance, d, between two points with polar coordinates (r1,θ1) and (r2,θ2) is

d=r12+r22−2r1r2cos(θ1−θ2).

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Chapter 6.3, Problem 106PE

Chapter 6.3, Problem 108PE

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Chapter 6 Solutions

Blitzer: Precalculus Essentials_5 (5th Edition)

Ch. 6.1 - Check Point 1 Solve the triangle shown in Figure...Ch. 6.1 - Check Point 2 Solve triangle ABC if , and b = 12....Ch. 6.1 - Check Point 3 Solve triangle ABC if A = a = 33,...Ch. 6.1 - Prob. 4CP Ch. 6.1 - Prob. 5CP Ch. 6.1 - Check Point 6 Find the area of a triangle having...Ch. 6.1 - Prob. 7CP Ch. 6.1 - Fill in each blank so that the resulting statement...Ch. 6.1 - Prob. 2CVC Ch. 6.1 - Prob. 3CVC

Knowledge Booster

To prove: That the distance, d , between two points with polar coordinates ( r 1 , θ 1 ) and ( r 2 , θ 2 ) is d = r 1 2 + r 2 2 − 2 r 1 r 2 cos ( θ 1 − θ 2 ) .

To prove: That the distance, d, between two points with polar coordinates (r1,θ1) and (r2,θ2) is d=r12+r22−2r1r2cos(θ1−θ2).

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Chapter 6 Solutions

To prove: That the distance, d, between two points with polar coordinates (r1,θ1) and (r2,θ2) is

d=r12+r22−2r1r2cos(θ1−θ2).