Question

The polar co-ordinates of the point whose cartesian co-ordinates are as $(-1,-1)$, are

• A. $(\sqrt{2},\frac{\pi }{4})$
• B. $(\sqrt{2},\frac{3\pi }{4})$
• C. $(\sqrt{2},-\frac{\pi }{4})$
• D. $(\sqrt{2},-\frac{3\pi }{4})$

Answer 1

The correct option is D $(\sqrt{2},-\frac{3\pi }{4})$

$\tan \theta =-\frac{b}{a}=-1\Rightarrow \theta =-\frac{3\pi }{4}r=\sqrt{a^2+b^2}=\sqrt{2}$
Hence polar coordinates is $(\sqrt{2},-\frac{3\pi }{4}).$