Question

The Cartesian coordinates of the point whose polar coordinates are $(2,\frac{\pi }{6})$, are

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

Answer 1

The correct option is A $(\sqrt{3},1)$

Given $(r,\theta )\equiv (2,\frac{\pi }{6})$
We know that $x=r\cos \theta$ and $y=r\sin \theta$
$\Rightarrow x=2\cos \frac{\pi }{6}=2\times \frac{\sqrt{3}}{2}=\sqrt{3}$
$\Rightarrow y=2\sin \frac{\pi }{6}=2\times \frac{1}{2}=1$

$\therefore$ Cartesian coordinates are $(x,y)\equiv (\sqrt{3},1)$