What are the components of the vector between the origin and the polar coordinate $(5, \frac{- 11 π}{6})$ $(5, (-11pi)/6)$ ?

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What are the components of the vector between the origin and the polar coordinate $(5, \frac{- 11 π}{6})$ $(5, (-11pi)/6)$ ?

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Answer 1 · 2018-01-27T11:18:43

We can use $x = r cos (θ)$ $x=rcos(theta)$ and $y = r sin (θ)$ $y=rsin(theta)$ to convert to the polar point to rectangular:

$x = 5 cos (- \frac{11 π}{6}) = 5 (\frac{\sqrt{3}}{2}) = \frac{5 \sqrt{3}}{2}$ $x=5cos(-(11pi)/6)=5(sqrt(3)/2)=(5sqrt(3))/2$
$y = 5 sin (- \frac{11 π}{6}) = 5 (\frac{1}{2}) = \frac{5}{2}$ $y=5sin(-(11pi)/6)=5(1/2)=(5)/2$

So the rectangular form is $(\frac{5 \sqrt{3}}{2}, \frac{5}{2})$ $( (5sqrt(3))/2, (5)/2 )$ .

Since we're talking about the component form of the vector, the initial point is $(0, 0)$ $(0,0)$ .

The component form of the vector is $[\frac{5 \sqrt{3}}{2}, \frac{5}{2}]$ $[(5sqrt(3))/2, (5)/2 ]$ .

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What are the components of the vector between the origin and the polar coordinate $(5, \frac{- 11 π}{6})$ $(5, (-11pi)/6)$ ?

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