Question

The polar co-ordinates of a point (1, – $\sqrt{3}$) is –

• A. $\left( –2,\frac{2\pi}{3} \right)$
• B. $\left( 2,\frac{2\pi}{3} \right)$
• C. $\left( –2,–\frac{\pi}{3} \right)$
• D. None

Answer 1

Answer: (A)

$\left( –2,\frac{2\pi}{3} \right)$

Answer 2

(1, –$\sqrt{3}$)

r = $\sqrt{x^{2} + y^{2}}$ = $\sqrt{1 + 4}$ = 2

Now a = tan^–1 $\frac{|y|}{|x|}$

a = tan^–1 $\left( \frac{\sqrt{3}}{1} \right)$ = $\frac{\pi}{3}$

Point lies in IV quadrant

\ q = – a Ž q = – $\frac{\pi}{3}$

$\left( 2,–\frac{\pi}{3} \right)$or $\left( –2,\frac{2\pi}{3} \right)$