Explanation Given: P 1 = ( r 1 , θ 1 ) and P 2 = ( r 2 , θ 2 ) . Calculation: x = r cos θ y = r sin θ Then ( x 1 , y 1 ) ⇒ ( r 1 cos θ 1 , r 1 sin θ 1 ) ( x 2 , y 2 ) ⇒ ( r 2 cos θ 2 , r 2 sin θ 2 ) d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 = ( r 2 cos θ 2 − r 1 cos θ 1 ) 2 + ( r 2 sin θ 2 + r 1 sin θ 1 ) 2

Precalculus Enhanced with Graphing Utilities (7th Edition)

7th Edition

ISBN: 9780134119281

Author: Michael Sullivan, Michael Sullivan III

Publisher: PEARSON

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Question

Chapter 9.1, Problem 86AE

To determine

To show: That the formula for the distance $d$ between two points $P_{1} = (r_{1}, θ_{1})$ and $P_{2} = (r_{2}, θ_{2})$ is $d = \sqrt{r_{1}^{2} + r_{2}^{2} - 2 r_{1} r_{2} cos (θ_{2} - θ_{1})}$ .

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Chapter 9.1, Problem 85AE

Chapter 9.1, Problem 87DW

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Precalculus Enhanced with Graphing Utilities (7th Edition)

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Knowledge Booster

That the formula for the distance d between two points P 1 = ( r 1 , θ 1 ) and P 2 = ( r 2 , θ 2 ) is d = r 1 2 + r 2 2 − 2 r 1 r 2 cos ( θ 2 − θ 1 ) .

Solution Summary: The author explains that the formula for the distance d between two points P 1 = ( r 1, 1) and P 2 =

To show: That the formula for the distance $d$ between two points $P_{1} = (r_{1}, θ_{1})$ and $P_{2} = (r_{2}, θ_{2})$ is $d = \sqrt{r_{1}^{2} + r_{2}^{2} - 2 r_{1} r_{2} cos (θ_{2} - θ_{1})}$ .

Want to see the full answer?

Chapter 9 Solutions

Additional Math Textbook Solutions

That the formula for the distance d between two points P 1 = ( r 1 , θ 1 ) and P 2 = ( r 2 , θ 2 ) is d = r 1 2 + r 2 2 − 2 r 1 r 2 cos ( θ 2 − θ 1 ) .

Solution Summary: The author explains that the formula for the distance d between two points P 1 = ( r 1, 1) and P 2 =

To show: That the formula for the distance d between two points P 1 = ( r 1 , θ 1 ) and P 2 = ( r 2 , θ 2 ) is d = r 1 2 + r 2 2 − 2 r 1 r 2 cos( θ 2 − θ 1 ) .

Want to see the full answer?

Chapter 9 Solutions

Additional Math Textbook Solutions

To show: That the formula for the distance $d$ between two points $P_{1} = (r_{1}, θ_{1})$ and $P_{2} = (r_{2}, θ_{2})$ is $d = \sqrt{r_{1}^{2} + r_{2}^{2} - 2 r_{1} r_{2} cos (θ_{2} - θ_{1})}$ .