Question

Lay down the positions of the points whose polar coordinates are $(1,-{210}^o)$

Answer 1

Polar co-ordinates are $(1,-{210}^{\circ })=(1,-\pi -{30}^{\circ })$
Then, $r=1$ and $\theta =-\pi -{30}^o$

$x=rcos\theta =1\times cos(-\pi -{30}^{\circ })=\frac{-\sqrt{3}}{2}$
$y=rsin\theta =1\times sin(-\pi -{30}^{\circ })=\frac{1}{2}$
$\Rightarrow$ Cartesian co-ordinates are $(\frac{-\sqrt{3}}{2},\frac{1}{2})$