Question

If the polar coordinates of a point are $(6,\frac{\pi }{3})$, then the Cartesian coordinates are

• A. $(3,1)$
• B. $(1,3)$
• C. $(3\sqrt{3},3)$
• D. $(3,3\sqrt{3})$

Answer 1

The correct option is D $(3,3\sqrt{3})$

We know the conversion formula,
$x=r\cos \theta y=r\sin \theta$
Given : $r=6,\theta =\frac{\pi }{3}$
Now, $x=6\cos \frac{\pi }{3}=3$
$y=6\sin \frac{\pi }{3}=3\sqrt{3}$
Hence, the Cartesian coordinates are $(3,3\sqrt{3})$.