Question

Match the polar coordinates with the cartesian coordinates:

LIST-I	LIST-II
A) $(\sqrt{3},1)$	1. $(2,\frac{5\pi }{6})$
B) $(-\sqrt{3},1)$	2. $(2,\frac{11\pi }{6})$
C) $(-\sqrt{3},-1)$	3. $(2,\frac{\pi }{6})$
D) $(\sqrt{3},-1)$	4. $(2,\frac{7\pi }{6})$

The correct match of LIST-I from LIST-II is
A B C D

• A. 3 1 2 4
• B. 3 1 4 2
• C. 1 4 3 2
• D. 1 4 2 3

Answer 1

The correct option is B 3 1 4 2

$A)$ $x=\sqrt{3},y=1$
Hence
$r=\sqrt{3+1}=2$
Now, $\cos \theta =\frac{\sqrt{3}}{2}$
Hence
$\theta =\frac{\pi }{6}$
$B)$ $x=-\sqrt{3},y=1$
Hence
$r=\sqrt{3+1}=2$
Now, $\cos \theta =-\frac{\sqrt{3}}{2}$
Hence, $\theta =\frac{5\pi }{6}$
$C)$$x=-\sqrt{3},y=-1$
Hence
$r=\sqrt{3+1}=2$
Now, $\cos \theta =-\frac{\sqrt{3}}{2}$
and $\sin \theta =-\frac{1}{2}$
Hence, $\theta =\frac{7\pi }{6}$
$D)$ $x=\sqrt{3},y=-1$
Hence, $r=\sqrt{3+1}=2$
Now, $\sin \theta =-\frac{1}{2}$
Hence, $\theta =-\frac{\pi }{6},\frac{11\pi }{6}$