What are the components of the vector between the origin and the polar coordinate $(16, (7pi)/6)$ ?

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Answer 1 · 2016-12-30T13:14:10

$(-8sqrt3,-8)$ or $-8sqrt3hati-8hatj$ ,

Components of a vector between the origin and the polar coordinate $(r,theta)$ are $(xcostheta,ysintheta)$ .
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Here we have $r=16$ and $theta=(7pi)/6$

Hence components are $(16cos((7pi)/6), 16sin((7pi)/6))$

or $(16xx(-sqrt3/2),16xx(-1/2))$

or $(-8sqrt3,-8)$

We can also write it as $-8sqrt3hati-8hatj$ ,

where $hati$ and $hatj$ are unit vectors along $x$ -axis and $y$ -axis respectively.

What are the components of the vector between the origin and the polar coordinate (16, (7pi)/6)(16, (7pi)/6)?