Question

Lay down the positions of the points whose polar coordinates are $(-a,\frac{\pi }{6})$

Answer 1

Polar co-ordinates are $(-a,\frac{\pi }{6})$
Then, $r=-a$ and $\theta =\frac{\pi }{6}$
$x=rcos\theta =-acos\frac{\pi }{6}=-\frac{\sqrt{3}a}{2}$
$y=rsin\theta =-asin\frac{\pi }{6}=-\frac{a}{2}$
Thus, the Cartesian co-ordinates are $(-\frac{\sqrt{3}a}{2},-\frac{a}{2})$