$\text {The cartesian co-ordinates of the point whose polar co-ordinates are }\left(\frac{1}{2},…
$\text {The cartesian co-ordinates of the point whose polar co-ordinates are }\left(\frac{1}{2}, 120^{\circ}\right) \text { are }$
$\left(\frac{1}{4}, \frac{-\sqrt{3}}{4}\right)$
$\left(\frac{1}{4}, \frac{\sqrt{3}}{4}\right)$
$\left(\frac{-1}{4}, \frac{-\sqrt{3}}{4}\right)$
$\left(\frac{-1}{4}, \frac{\sqrt{3}}{4}\right)$
Solution
Given $\mathrm{P}(\mathrm{r}, \theta)=\left(\frac{1}{2}, 120^{\circ}\right) \Rightarrow \mathrm{r}=\frac{1}{2}, \theta=120^{\circ}$
We have $\mathrm{x}=\mathrm{r} \cos \theta=\frac{1}{2} \cos 120^{\circ} \quad=\frac{1}{2}\left(-\frac{1}{2}\right) \Rightarrow \mathrm{x}=-\frac{1}{4}$
and $y=r \sin \theta=\frac{1}{2} \sin 120^{\circ}=\frac{1}{2}\left(\frac{\sqrt{3}}{2}\right)=\frac{\sqrt{3}}{4}$
$\therefore$ Required point is $\mathrm{P}\left(-\frac{1}{4}, \frac{\sqrt{3}}{4}\right)$