What are the components of the vector between the origin and the polar coordinate $(-16, (-pi)/4)$ ?

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Answer 1 · 2018-02-27T05:06:53

$x = -16 * cos (-pi/4 )= -16 * (1/sqrt2) = color (green)(-8sqrt2$

$y = -16 * sin (-pi/4 )= -16 * (-1/sqrt2) = color (green)(8sqrt2$

We can use the following formulas to convert polar to Cartesian coordinates.

$x = r cos theta, y = r sin theta$

$Given : [r,theta] = [-16, -pi/4]$

$x = -16 * cos (-pi/4 )= -16 * (1/sqrt2) = color (green)(-8sqrt2$

$y = -16 * sin (-pi/4 )= -16 * (-1/sqrt2) = color (green)(8sqrt2$

$tan theta = tan (-pi/4) = -1$

What are the components of the vector between the origin and the polar coordinate (-16, (-pi)/4)(-16, (-pi)/4)?