Question

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

• 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 $(\sqrt{2},-\frac{3\pi }{4})$

Rectangular to polar coordinate, $(x,y)⟶(r,\theta )$

radius,r can be found by using , $r=\sqrt{x^2+y^2}r=\sqrt{(-1{)}^2+(-1{)}^2}=\sqrt{2}$

$\theta$ can be found using the reference angle:$\tan \theta =\frac{y}{x}\tan \theta =\frac{-1}{-1}⟹\tan \theta =1⟹\theta ={\tan }^{-1}1=\theta =\frac{-3\pi }{4}$

As the point (-1-1) lies at Quadrant

iii)i.e, $\theta =\frac{-3\pi }{4}$

From $(r,\theta )=(\sqrt{2},\frac{-3\pi }{4})$