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

Finley Mckinney

Finley Mckinney

Answered question

2022-06-22

What is the distance between the following polar coordinates?: ( 7 , 5 π 4 ) , ( 2 , 9 π 8 )

Answer & Explanation

laure6237ma

laure6237ma

Beginner2022-06-23Added 27 answers

Step 1
P 1 P 2 = r 1 2 + r 2 2 - 2 r 1 r 2 cos ( θ 2 - θ 1 )
r 1 = 7 , θ 1 = 5 π 4 ; r 2 = 2 , θ 2 = 9 π 8
P 1 P 2 = 7 2 + 2 2 - 2 7 2 cos ( 9 π 8 - 5 π 4 )
Step 2
P 1 P 2 = 49 + 4 - 28 cos ( - π 8 )
P 1 P 2 = 53 - 28 cos ( π 8 ) 5.209
Eden Solomon

Eden Solomon

Beginner2022-06-24Added 7 answers

Step 1
r 1 = 7
r 2 = 2
θ 1 = 5 π 4
θ 2 = 9 π 8
θ 2 - θ 1 = 9 π 8 - 5 π 4 = 9 π - 10 π 8 = - π 8
cos ( - π 8 ) = 0 , 9
s = r 1 2 + r 2 2 - 2 r 1 r 2 cos ( θ 2 - θ 1 )
Step 2
s = 7 2 + 2 2 - 2 7 2 0 , 9
s = 49 + 4 - 28 0 , 9
s = 53 - 25.2
s = 27 , 8
s 5.27

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