What are the components of the vector between the origin and the polar coordinate $(-5, (-3pi)/4)$ ?

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Answer 1 · 2018-02-27T06:00:41

Rectangular coordinates are $color(indigo)((3.5355, 3.5355)$ or $color(indigo)((5/sqrt2, 5/sqrt2)$

Given $r = -5, theta = -(3pi)/4$

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To find the Cartesian coordinates.

$x = r cos theta = -5 * cos ((-3pi)/4) = color(indigo)(3.5355)$

$y = r sin theta = -5 * sin ((-3pi)/4) = color(indigo)(3.5355)$

What are the components of the vector between the origin and the polar coordinate (-5, (-3pi)/4)(-5, (-3pi)/4)?