What are the components of the vector between the origin and the polar coordinate $(3, (19pi)/12)$ ?

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Answer 1 · 2018-02-23T07:00:38

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$Given r = 3, theta = (19pi)/12$

To find components of the vector between origin and the given point (3,(19pi)/12#

$theta =( (19pi)/12)^c = 285^@$

$x = r cos theta = 3 * cos ((19pi)/12) = 0.7765$

$y = r sin theta = 3 * sin ((19pi)/12) = -2.8978$

$tan theta = tan ((19pi)/12) = y / x = - 2.8978 / 0.7765 = -3.7321$

In rectangular form $(x,y) = (0.7765, -2.8978)$

In polar form $(r, theta) = (3, (19pi)/12)$

Slope of the vector m = tan theta = - 3.7321#

Vector is in the IV quadrant.

What are the components of the vector between the origin and the polar coordinate (3, (19pi)/12)(3, (19pi)/12)?