Answer:
[tex]\displaystyle (x,y)\rightarrow\biggr(\frac{5\sqrt{3}}{2},\frac{5}{2}\biggr)[/tex]
Step-by-step explanation:
We are given polar coordinates of [tex](r,\theta)\rightarrow(5,30^\circ)[/tex] and wish to convert them to rectangular coordinates in the form of [tex](x,y)[/tex]. Use the formulas [tex]x=r\cos\theta[/tex] and [tex]y=r\sin\theta[/tex] to convert:
[tex]\displaystyle x=r\cos\theta\\\\x=5\cos30^\circ\\\\x=5\biggr(\frac{\sqrt{3}}{2}\biggr)\\\\x=\frac{5\sqrt{3}}{2}[/tex]
[tex]\displaystyle y=r\sin\theta\\\\y=5\sin30^\circ\\\\y=5\biggr(\frac{1}{2}\biggr)\\\\y=\frac{5}{2}[/tex]
Thus, the rectangular coordinates of [tex](r,\theta)\rightarrow(5,30^\circ)[/tex] are [tex]\displaystyle (x,y)\rightarrow\biggr(\frac{5\sqrt{3}}{2},\frac{5}{2}\biggr)[/tex].
