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

fabios3

fabios3

Answered question

2022-06-24

What is the distance between the following polar coordinates?:
( 5 , 7 π 4 ) , ( 9 , 11 π 8 )

Answer & Explanation

last99erib

last99erib

Beginner2022-06-25Added 19 answers

Step 1
Distance between tow points knowing the polar coordinates is given by the formula using cosine rule
d = r 1 2 + r 2 2 - 2 r 1 r 2 cos ( θ 2 - θ 1 )
Given r 1 = 5 , r 2 = 9 , θ 1 = ( 7 π 4 ) c , θ 2 = ( 11 π 8 ) c
d = 5 2 + 9 2 - ( 2 5 9 cos ( 11 π 8 - 7 π 4 ) )
d = 106 - 90 cos ( - 3 π 8 ) 8.4592

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