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

lobht98 2022-06-16 Answered
What is the distance between the following polar coordinates?: ( 1 , π 4 ) , ( 12 , 9 π 8 )
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Answers (1)

zalitiaf
Answered 2022-06-17 Author has 27 answers
Step 1
Distance between two polar coordinates formula
d = r 1 2 + r 2 2 - 2 r 1 r 2 cos ( θ 2 - θ 1 )
Solution:
Let ( r 1 , θ 1 ) = ( 1 , π 4 )
Let ( r 2 , θ 2 ) = ( 12 , 9 π 8 )
Use
d = r 1 2 + r 2 2 - 2 r 1 r 2 cos ( θ 2 - θ 1 )
d = 1 2 + 12 2 - 2 ( 1 ) ( 12 ) cos ( 9 π 8 - π 4 )
d = 145 - 24 cos ( 7 π 8 )
d = 12.92954402832 units
God bless. I hope the explanation is useful.
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