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

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Answer 1 · 2016-04-07T14:46:29

$(-5 cos (pi/12), -5 sin(pi/12)) = (-4.83, -1.39)$ , nearly.

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

Here, r = 5 and $theta = - 13pi/12=pi+pi/12$ (in the third quadrant)..

$cos (pi+pi/12)=-cos(pi/12) and sin (pi+pi/12)=-sin(pi/12)$ .

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

What are the components of the vector between the origin and the polar coordinate (5, (13pi)/12)(5, (13pi)/12)?