What are the components of the vector between the origin and the polar coordinate $(-7, (-pi)/4)$ ?

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Answer 1 · 2017-11-14T09:34:57

$(-7sqrt(2))/2 hati +(7sqrt(2))/2 hatj$

This is much easier to solve if you convert the polar coordinates into Cartesian coordinates first. This can be achieved using:

$x=rcostheta$

$y=rsintheta$

$x=-7cos((-pi)/4)=(-7sqrt(2))/2$

$y=-7sin((-pi)/4)=(7sqrt(2))/2$

Cartesian coordinates:

$((-7sqrt(2))/2 , (7sqrt(2))/2 )$