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:

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

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

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