What are the components of the vector between the origin and the polar coordinate $(6, pi/3)$ ?

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Answer 1 · 2018-03-25T17:16:38

$(3,3sqrt(3))$

The coordinates of the vector are the rectangular coordinates.

So let's convert the polar coordinates to rectangular form using the formula:

$(r, theta)->(x,y)$

$x=rcostheta$
$y=rsintheta$

$x=(6)cos(pi/3)=6(1/2)=3$

$y=(6)sin(pi/3)=6(sqrt(3)/2)=3sqrt(3)$

So the vector components are $(3, 3sqrt(3))$

What are the components of the vector between the origin and the polar coordinate (6, pi/3)(6, pi/3)?