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

Taniyah Estrada 2022-06-25 Answered
What is the distance between the following polar coordinates?: ( 7 , 5 π 4 ) , ( 3 , 13 π 8 )
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Answers (1)

robegarj
Answered 2022-06-26 Author has 24 answers
Step 1
using the polar version of the distance formula
d 2 = r 1 2 + r 2 2 - [ 2 r 1 r 2 cos ( θ 2 - θ 1 ) ]
Let ( r 1 , θ 1 ) = ( 7 , 5 π 4 ) and ( r 2 , θ 2 ) = ( 3 , 13 π 8 )
Step 2
d 2 = 7 2 + 3 2 - [ 2 × 7 × 3 cos ( 13 π 8 - 5 π 4 ) ]
d 2 = 49 + 9 - ( 42 cos ( 3 π 8 ) )
d = 58 - 42 cos ( 3 π 8 ) 6.475
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