Question

37Convert the polar coordinate, ( 6,2to a rectangular coordinate (Ex, Ey).[ Select ]x=[Select][ Select ]y =

Answer 1

Polar coordinates are generally written as :

`(r,\theta)`

And the rectangular coordinate equivalent (x,y) is obtained using the following relationships:

`\begin{gathered} x=\text{ r}*\cos \theta \\ y=r*\sin \theta \end{gathered}`

Now, since the given polar coordinate is:

`\begin{gathered} (r,\theta) \\ \Longrightarrow\text{ (6, }(3\pi)/(2)\text{)} \\ r=\text{ 6,} \\ \theta=(3\pi)/(2) \end{gathered}`

Therefore, the corresponding rectangular coordinate is :

`\begin{gathered} x=\text{ r}*\cos \theta \\ y=\text{ r}*\sin \theta \\ =>x=6*\cos ((3\pi)/(2))\text{ (note: }(3\pi)/(2)radians=270^o\text{)} \\ x=\text{ 6 }* cos270^o=6\text{ }*0\text{ = 0} \\ x=\text{ 0} \\ \Rightarrow y=6*\sin ((3\pi)/(2)) \\ y=\text{ 6}*\sin 270^o \\ y=\text{ 6}*(-1)\text{ = -6} \\ y=\text{ -6} \end{gathered}`

Therefore, the rectangular coordinate equivalent (x,y) is (0,-6)