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

1 Answer
Jul 11, 2017

#~~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.