Question

If cartesian co-ordinates of any point are $(\sqrt{3},1)$, then its polar co-ordinates is

• A. $(2,\pi/3)$
• B. $(\sqrt{2},\pi/6)$
• C. $(2,\pi/6)$
• D. None of these

Answer 1

Answer: (C)

$(2,\pi/6)$

Answer 2

We know that $x = r\cos\theta$, $y = r\sin\theta$

$\therefore$ $\sqrt{3} = r\cos\theta,$ $1 = r\sin\theta$

$r = \sqrt{(\sqrt{3})^{2} + (1)^{2}} = 2$, $\theta = \tan^{- 1}\left( \frac{1}{\sqrt{3}} \right) = \pi/6$

Polar co-ordinates $= (2,\pi/6)$.