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

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Answer 1 · 2018-03-25T17:16:38

$(3, 3 \sqrt{3})$ $(3,3sqrt(3))$

The coordinates of the vector are the rectangular coordinates.

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

$(r, θ) \to (x, y)$ $(r, theta)->(x,y)$

$x = r cos θ$ $x=rcostheta$
$y = r sin θ$ $y=rsintheta$

$x = (6) cos (\frac{π}{3}) = 6 (\frac{1}{2}) = 3$ $x=(6)cos(pi/3)=6(1/2)=3$

$y = (6) sin (\frac{π}{3}) = 6 (\frac{\sqrt{3}}{2}) = 3 \sqrt{3}$ $y=(6)sin(pi/3)=6(sqrt(3)/2)=3sqrt(3)$

So the vector components are $(3, 3 \sqrt{3})$ $(3, 3sqrt(3))$

What are the components of the vector between the origin and the polar coordinate (6, pi/3)(6,π3)(6, pi/3)?