What is the distance between the following polar coordinates?: # (3,(-4pi)/3), (4,(-5pi)/6) #

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Answer 1 · 2017-04-16T00:51:33

#5#

First, write the polar coordinates in cartesian form. You will need the parametric form to help you with that:

#x=rcostheta#

#y=rsintheta#

Plug in for the first point:

#x=3cos(-4pi/3)=-1.5#

#y=3sin(-4pi/3)=(3sqrt3)/2#

Plug in for the second point:

#x=4cos(-5pi/6)=-2sqrt(3)#

#y=4sin(-5pi/6)=-2#

So now we have the two points: #(-1.5,3sqrt3)/2)# and #(-2sqrt(3),-2)#. Now use the distance formula:

#d=sqrt((-2sqrt(3)-(-1.5))^2+ (-2-(3sqrt3)/2)^2=5#