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

Hailee Stout

Hailee Stout

Answered question

2022-05-11

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

Answer & Explanation

Cecelia Mullins

Cecelia Mullins

Beginner2022-05-12Added 10 answers

Step 1
The distance formula for polar coordinates is
d = r 1 2 + r 2 2 - 2 r 1 r 2 cos ( θ 1 - θ 2 )
Where d is the distance between the two points, r 1 , and θ 1 are the polar coordinates of one point and r 2 and θ 2 are the polar coordinates of another point.
Let ( r 1 , θ 1 ) represent ( 4 , 7 π 4 ) and ( r 2 , θ 2 ) represent ( 3 , 3 π 8 )
d = 4 2 + 3 2 - 2 4 3 cos ( 7 π 4 - 3 π 8 )
d = 16 + 9 - 24 cos ( 11 π 8 )
d = 25 - 24 ( - 0.3847 ) = 25 + 9.2328 = 34.2328 = 5.8508 units
d = 5.8508 units (approx)
Hence the distance between the given points is 5.8508

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?