Given the Polar Coordinates:
[tex]\mleft(9,150\degree\mright)[/tex]You need to use the following formulas:
[tex]\begin{gathered} x=r\cdot cos\theta \\ \\ y=r\cdot\sin \theta \end{gathered}[/tex]Remember that Polar Coordinates have this form:
[tex](r,\theta)[/tex]And Rectangular Coordinates have this form:
[tex](x,y)[/tex]In this case, you can identify that:
[tex]\begin{gathered} r=9 \\ \theta=150\text{\degree} \end{gathered}[/tex]Therefore, you can substitute values into the formulas:
[tex]\begin{gathered} x=9\cdot cos(150\text{\degree)} \\ \\ y=9\cdot sin(150\text{\degree)} \end{gathered}[/tex]Evaluating, you get:
[tex]\begin{gathered} x=-\frac{9\sqrt[]{3}}{2} \\ \\ y=\frac{9}{2} \end{gathered}[/tex]Hence, the answer is:
[tex](-\frac{9\sqrt[]{3}}{2},\frac{9}{2})[/tex]