Question

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

Answer 1

`~~8.61`

Explanation:

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`:

`(3pi)/4 - pi/8 =(6pi)/8 - pi/8=(5pi)/8`

`c^2=a^2+b^2-2ab cos C`
`c^2=7^2+3^2-2(7)(3) cos ((5pi)/8)`
`c^2=58-42 cos ((5pi)/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.