Find the Cartesian co-ordinates of point whose polar co-ordinates… - Vidyadip

Question

Find the Cartesian co-ordinates of point whose polar co-ordinates are $\left(4, \frac{\pi}{3}\right)$

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Answer

$
(r, \theta)=\left(4, \frac{\pi}{3}\right)
$
Using $x=r \cos \theta$ and $y=r \sin \theta$, where $(x, y)$ are the required Cartesian co-ordinates, we get $x=4 \cos \left(\frac{\pi}{3}\right)$ and $y=4 \sin \left(\frac{\pi}{3}\right)$
$\therefore x=4\left(\frac{1}{2}\right)$ and $y=4\left(\frac{\sqrt{3}}{2}\right)$
$\therefore x=2$ and $y=2 \sqrt{3}$
$\therefore$ The required Cartesian co-ordinates are $(2,2 \sqrt{3})$.

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