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:

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

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

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