What are the rectangular coordinates of (3, -π/3)?

$x = \frac{3}{2}$
$y = \frac{- 3 \sqrt{3}}{2}$

Explanation:

From the given: $r = 3$ and $\theta = - \frac{\pi}{3}$

$x = r \cdot \cos \theta$
$x = 3 \cdot \cos \left(- \frac{\pi}{3}\right)$
$x = 3 \cdot \left(\frac{1}{2}\right)$
$x = \frac{3}{2}$

$y = r \cdot \sin \theta$
$y = 3 \cdot \sin \left(- \frac{\pi}{3}\right)$
$y = 3 \cdot \frac{- \sqrt{3}}{2}$

$y = \frac{- 3 \sqrt{3}}{2}$

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