What are the components of the vector between the origin and the polar coordinate $(5, \frac{13 π}{12})$ $(5, (13pi)/12)$ ?

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What are the components of the vector between the origin and the polar coordinate $(5, \frac{13 π}{12})$ $(5, (13pi)/12)$ ?

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Answer 1 · 2016-04-07T14:46:29

$(- 5 cos (\frac{π}{12}), - 5 sin (\frac{π}{12})) = (- 4.83, - 1.39)$ $(-5 cos (pi/12), -5 sin(pi/12)) = (-4.83, -1.39)$ , nearly.

Explanation:

The components of the radial vector to (r, $θ$ $theta$ ) are $(x, y) = (r cos θ, r sin θ)$ $(x, y) = (r cos theta, r sin theta)$ .

Here, r = 5 and $θ = - 13 \frac{π}{12} = π + \frac{π}{12}$ $theta = - 13pi/12=pi+pi/12$ (in the third quadrant)..

$cos (π + \frac{π}{12}) = - cos (\frac{π}{12}) and sin (π + \frac{π}{12}) = - sin (\frac{π}{12})$ $cos (pi+pi/12)=-cos(pi/12) and sin (pi+pi/12)=-sin(pi/12)$ .

So, the components (x, y) = $(- 5 cos (\frac{π}{12}), - 5 sin (\frac{π}{12})) = (- 4.83, - 1.39)$ $(-5 cos (pi/12), -5 sin(pi/12)) = (-4.83, -1.39)$ , nearly.

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What are the components of the vector between the origin and the polar coordinate $(5, \frac{13 π}{12})$ $(5, (13pi)/12)$ ?

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Explanation:

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What are the components of the vector between the origin and the polar coordinate $(5, \frac{13 π}{12})$ $(5, (13pi)/12)$ ?