What is the distance between the following polar coordinates?: # (5,(19pi)/12), (3,(11pi)/8) #

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Answer 1 · 2017-04-16T00:42:18

#3.130#

First, write each polar coordinate as cartesian coordinates. Use the parametric form to write #x# and #y#:

#x=rcos(theta)#

#y=rsin(theta)#

Plug in for the first point:

#x=5cos(19pi/12)~~1.294#

#y=5sin(19pi/12)~~-4.830#

Plug in for the second point:

#x=3cos(11pi/8)~~-1.148#

#y=3sin(11pi/8)~~-2.772#

So we have the two points in the cartesian form: #(1.294,-4.830)# and #(-1.148,-2.772)#. Now we can use the distance formula:

#d=sqrt((-1.148-1.294)^2+(-2.772-(-4.830))^2~~3.130#