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

Rapsinincke

Rapsinincke

Answered

2022-07-04

What is the distance between the following polar coordinates?: ( 3 , π 4 ) , ( 9 , 3 π 8 )

Answer & Explanation

Wade Atkinson

Wade Atkinson

Expert

2022-07-05Added 12 answers

Step 1
If the points are P ( 2 ,   π 4 ) and Q ( 9 ,   3 8 π ) and O is the pole r = 0 , then
Length P Q = O Q 2 + G P 2 - 2 ( O P ) ( O Q ) cos Q O P
= 9 2 + 2 2 - 2 ( 9 ) ( 2 ) cos ( 3 8 π - π 4 )
= 85 - 36 cos ( π 8 )
= 85 - 36 ( 1 - cos ( π 4 ) 2 )
= 85 - 36 1 - 1 2 2 )
= 8.4394 , nearly.

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