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

sedeln5w

sedeln5w

Answered question

2022-06-20

What is the distance between the following polar coordinates?: ( 3 , 3 π 4 ) , ( 2 , 7 π 8 )

Answer & Explanation

Xzavier Shelton

Xzavier Shelton

Beginner2022-06-21Added 26 answers

Step 1
We can do this by converting each coordinate to the equivalent Cartesian (rectangular) form, and using the distance formula:
x = r cos θ
y = r sin θ
x 1 = 3 cos ( 3 π 4 ) = - 2.121
y 1 = 3 sin ( 3 π 4 ) = 2.121
x 2 = 2 cos ( 7 π 8 ) = - 1.848
y 2 = 2 sin ( 7 π 8 ) = 0.765
distance = ( - 2.121 - ( - 1.848 ) ) 2 + ( 2.121 - 0.765 ) 2
= 1.383 units

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