What is the distance between the following polar coordinates?: # (1,pi/3), (-1,pi/2) #

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Answer 1 · 2015-11-29T21:05:43

These are both on the unit circle.

Since #pi/2# is #90^o#, but the #-1# moves it #180^o# from (0,1) to (0,-1)

The point #(-1,pi/2)# is at #(0,-1)#

#pi/3=60^o#, therefore ...
#x=cos60=1/2# and #y=sin60=sqrt3/2~~0.8660#

So, the point #(1,pi/3)# is at #~~(1/2,0.8660)#

Using the distance formula :

distance #=sqrt[(1/2-0)^2+(sqrt3/2+1)^2]=sqrt(2+sqrt3)~~1.9#

hope that helped

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