Find the polar co-ordinates of points whose Cartesian co-ordinate… - Vidyadip

Question

Find the polar co-ordinates of points whose Cartesian co-ordinates are : $(-1,-1)$

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Answer

$(x, y)=(-1,-1)$
$ \therefore r=\sqrt{x^2+y^2}=\sqrt{1+1}=\sqrt{2}$
$\tan \theta=\frac{y}{x}=\frac{-1}{-1}=1$
$\therefore \tan \theta=\tan \frac{\pi}{4} $
Since the given point lies in the $3$ rd quadrant,
$ \tan \theta=\tan \left(\pi+\frac{\pi}{4}\right) \ldots[\because \tan (n+x)=\tan x]$
$\therefore \tan \theta=\tan \left(\frac{5 \pi}{4}\right)$
$\therefore \theta=\frac{5 \pi}{4}=225^{\circ}$
$\therefore$ the required polar co-ordinates are $\left(\sqrt{2}, 225^{\circ}\right)$.

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