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

Ezekiel Yoder

Ezekiel Yoder

Answered question

2022-06-11

What is the distance between the following polar coordinates?:
( 11 , 17 π 12 ) , ( 4 , π 8 )

Answer & Explanation

ejigaboo8y

ejigaboo8y

Beginner2022-06-12Added 29 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 = 11 , r 2 = 4 , θ 1 = ( 17 π 12 ) c , θ 2 = ( π 8 ) c
d = 11 2 + 4 2 - ( 2 11 4 cos ( π 8 - 17 π 12 ) )
d = 137 - 88 cos ( - 31 π 24 ) 13.8047

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