What are the components of the vector between the origin and the polar coordinate $(6, (5pi)/4)$ ?

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Answer 1 · 2018-03-19T01:02:04

$<-3sqrt(2), -3sqrt(2)>$

Given: polar coordinates $(6, (5 pi)/4)$

To convert from polar to rectangular form use:

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

$(6, (5 pi)/4) = (r, theta)$

The angle $(5 pi)/4$ is in the third quadrant, $45^@$ past $180^@.$

$sin (5 pi)/4 = -sqrt(2)/2$

$cos (5 pi)/4 = -sqrt(2)/2$

$x = 6 * -sqrt(2)/2 = -3 sqrt(2)$

$y = 6 * -sqrt(2)/2 = -3 sqrt(2)$

The vector from the origin (0,0) to the point $(x, y)$ is

$<-3sqrt(2), -3sqrt(2)>$

What are the components of the vector between the origin and the polar coordinate (6, (5pi)/4)(6, (5pi)/4)?