What are the components of the vector between the origin and the polar coordinate #(-1, (4pi)/3)#?

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Answer 1 · 2017-11-19T11:03:52

#1/2hati+sqrt(3)/2hatj#

First we need to convert the polar coordinates into Cartesian coordinates. We can do this using:

#x= rcostheta#
#y= rsintheta#

#x= -1cos((4pi)/3)=1/2#

#y= -1sin((4pi)/3)=sqrt(3)/2#

Cartesian coordinates:

#( 1/2 , sqrt(3)/2 )#

#1/2hati+sqrt(3)/2hatj#