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

Yahir Crane

Yahir Crane

Answered question

2022-06-26

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

Answer & Explanation

Kaydence Washington

Kaydence Washington

Beginner2022-06-27Added 32 answers

Step 1
You can use the Law of Cosines.
If you plot the polar coordinates and draw lines from the origin to the points, you will have 2 sides of a triangle. The 3rd side will be the distance between the 2 points.
Find the angle C:
3 π 4 - π 8 = 6 π 8 - π 8 = 5 π 8
c 2 = a 2 + b 2 - 2 a b cos C
c 2 = 7 2 + 3 2 - 2 ( 7 ) ( 3 ) cos ( 5 π 8 )
c 2 = 58 - 42 cos ( 5 π 8 )
c 2 74.07
c 8.61
You can also solve this problem by converting the polar coordinates to rectangular coordinates and using the distance formula.

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