What are the components of the vector between the origin and the polar coordinate $(15, (-3pi)/4)$ ?

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Answer 1 · 2017-11-29T18:21:24

$-(15sqrt(2))/2hati-(15sqrt(2))/2hatj$

First convert the polar coordinate in a Cartesian coordinate. This can be done using:

$x=rcos(theta)$

$y=rsin(theta)$

$x= 15cos(-(3pi)/4)=-(15sqrt(2))/2$

$y= 15sin(-(3pi)/4)=-(15sqrt(2))/2$

Cartesian coordinates:

$(-(15sqrt(2))/2 , -(15sqrt(2))/2 )$

Vector components.

$x=-(15sqrt(2))/2hati$

$y=-(15sqrt(2))/2hatj$

$:.$

$-(15sqrt(2))/2hati-(15sqrt(2))/2hatj$

What are the components of the vector between the origin and the polar coordinate (15, (-3pi)/4)(15, (-3pi)/4)?