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

Karina Trujillo 2022-06-24 Answered
What is the distance between the following polar coordinates?:
( 9 , 17 π 12 ) , ( 4 , 3 π 8 )
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Answers (1)

scipionhi
Answered 2022-06-25 Author has 25 answers
Step 1
Plotting these two points, there is a triangle formed whose central angle measures
3 π 8 + 7 π 12 = 23 π 24
By the Law of Cosines, the distance, c, between the points is found by
c 2 = 9 2 + 4 2 - ( 9 ) ( 4 ) cos ( 23 π 24 )
That is
c 2 = 97 - 36 cos ( 23 π 24 )
The value of c is the positive square root of the expression on the right side.

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