Given
Polar coordinates
[tex](-3,\frac{\Pi}{6})[/tex]
Find
convert it into cartesian coordinates
Explanation
As, it is in a polar form , so we use following formulas to convert it into cartesian coordinates
[tex]\begin{gathered} x=rcos\theta \\ y=rsin\theta \end{gathered}[/tex]
as, we have given
[tex]r=-3\text{ and }\theta=\frac{\Pi}{6}[/tex]
so,
[tex]\begin{gathered} x=-3cos(\frac{\Pi}{6})=-3\times\frac{\sqrt{3}}{2}=-\frac{3\sqrt{3}}{2} \\ y=-3sin(\frac{\Pi}{6})=\text{ -3}\times\frac{1}{2}=-\frac{3}{2} \end{gathered}[/tex]
so, the cartesian coordinates are
[tex](-\frac{3\sqrt{3}}{2},\text{ -}\frac{3}{2})[/tex]
Final Answer
Therefore the cartesian coordinates are
[tex](-\frac{3\sqrt{3}}{2},\text{ -}\frac{3}{2})[/tex]
