Polar coordinates are generally written as :
[tex](r,\theta)[/tex]
And the rectangular coordinate equivalent (x,y) is obtained using the following relationships:
[tex]\begin{gathered} x=\text{ r}\times\cos \theta \\ y=r\times\sin \theta \end{gathered}[/tex]
Now, since the given polar coordinate is:
[tex]\begin{gathered} (r,\theta) \\ \Longrightarrow\text{ (6, }\frac{3\pi}{2}\text{)} \\ r=\text{ 6,} \\ \theta=\frac{3\pi}{2} \end{gathered}[/tex]
Therefore, the corresponding rectangular coordinate is :
[tex]\begin{gathered} x=\text{ r}\times\cos \theta \\ y=\text{ r}\times\sin \theta \\ =>x=6\times\cos (\frac{3\pi}{2})\text{ (note: }\frac{3\pi}{2}radians=270^o\text{)} \\ x=\text{ 6 }\times cos270^o=6\text{ }\times0\text{ = 0} \\ x=\text{ 0} \\ \Rightarrow y=6\times\sin (\frac{3\pi}{2}) \\ y=\text{ 6}\times\sin 270^o \\ y=\text{ 6}\times(-1)\text{ = -6} \\ y=\text{ -6} \end{gathered}[/tex]
Therefore, the rectangular coordinate equivalent (x,y) is (0,-6)
