What are the components of the vector between the origin and the polar coordinate #(-5, (2pi)/3)#?

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Answer 1 · 2017-11-14T21:01:22

#-5/2hati-(5sqrt(3))/2hatj#

First we need to convert the polar coordinates into Catresian coordinates. We can do this with the following:

#x=rcostheta#

#y=rsintheta#

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

#y=-5sin((2pi)/3)=(-5sqrt(3))/2#

Cartesian coordinate:

#( -5/2 , (-5sqrt(3))/2 )#

#-5/2hati-(5sqrt(3))/2hatj#