What are the components of the vector between the origin and the polar coordinate $(9, \frac{- π}{4})$ $(9, (-pi)/4)$ ?

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What are the components of the vector between the origin and the polar coordinate $(9, \frac{- π}{4})$ $(9, (-pi)/4)$ ?

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Answer 1 · 2016-03-25T13:08:49

$x = \frac{9 \sqrt{2}}{2}$ $x=(9sqrt2)/2$
$y = \frac{- 9 \sqrt{2}}{2}$ $y=(-9sqrt2)/2$

Explanation:

Given $(r, θ) = (9, - \frac{π}{4})$ $(r, theta)=(9, -pi/4)$

$x = r cos θ = 9 \cdot cos (- \frac{π}{4})$ $x=r cos theta=9*cos (-pi/4)$
$x = 9 \cdot \frac{1}{\sqrt{2}} = \frac{9}{\sqrt{2}} = \frac{9 \cdot \sqrt{2}}{{(\sqrt{2})}^{2}} = \frac{9 \sqrt{2}}{2}$ $x=9*1/sqrt2=9/sqrt2=(9*sqrt2)/(sqrt2)^2=(9sqrt2)/2$

$y = r sin θ = 9 \cdot sin (- \frac{π}{4})$ $y=r sin theta=9*sin (-pi/4)$
$y = 9 \cdot - \frac{1}{\sqrt{2}} = - \frac{9}{\sqrt{2}} = \frac{- 9 \cdot \sqrt{2}}{{(\sqrt{2})}^{2}} = \frac{- 9 \sqrt{2}}{2}$ $y=9*-1/sqrt2=-9/sqrt2=(-9*sqrt2)/(sqrt2)^2=(-9sqrt2)/2$

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What are the components of the vector between the origin and the polar coordinate $(9, \frac{- π}{4})$ $(9, (-pi)/4)$ ?

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Explanation:

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What are the components of the vector between the origin and the polar coordinate $(9, \frac{- π}{4})$ $(9, (-pi)/4)$ ?