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 : $(5,5)$

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Answer

$ \text { i. }(x, y)=(5,5)$
$\therefore r=\sqrt{x^2+y^2}=\sqrt{25+25}$
$=\sqrt{50}=5 \sqrt{2}$
$\tan \theta=\frac{y}{x}=\frac{5}{5}=1 $
Since the given point lies in the 1st quadrant,
$\theta=45^{\circ} \ldots\left[\because \tan 45^{\circ}=1\right]$
$\therefore$ the required polar co-ordinates are $\left(5 \sqrt{2}, 45^{\circ}\right)$.

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