What is the distance between the following polar coordinates?: <mstyle displaystyle="true">

oplodnjomqunfs

oplodnjomqunfs

Answered question

2022-06-03

What is the distance between the following polar coordinates?:
( 5 , 3 π 4 ) , ( 3 , 11 π 8 )

Answer & Explanation

lifeinjerseyjwapj

lifeinjerseyjwapj

Beginner2022-06-04Added 2 answers

Step 1
If two polar points A = ( r 1 , φ 1 ) and B = ( r 2 , φ 2 ) are given, then the distance between the points can be calculated as:
d ( A , B ) = r 1 2 + r 2 2 - 2 r 1 r 2 cos ( φ 2 - φ 1 )
Here we have:
d = 5 2 + 3 2 - 2 5 3 cos ( 11 π 8 - 3 π 4 ) =
= 25 + 9 - 30 cos ( 11 π - 6 π 8 ) =
= 34 - 30 cos ( 5 π 8 ) 34 - 30 ( - 0.383 )
34 + 11.49 45.49 6.74

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