Question

Check the image I got y=-xsqrt3/3 but I want to double check

Answer 1

To convert the polar equation to a rectangular equation .

Given polar equation is,

`\theta=(11\pi)/(6)`

we know the convertion of polar coordinates (r,theta) to rectangular equation as,

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

we get,

`\theta=(11\pi)/(6)=(2\pi-(\pi)/(6))`

Substitute this in the above equation we get,

`\begin{gathered} x=r\cos (2\pi-(\pi)/(6)) \\ \\ y=r\sin (2\pi-(\pi)/(6)) \end{gathered}`

Solving we get,

`\begin{gathered} x=r\cos ((\pi)/(6)) \\ \\ y=-r\sin ((\pi)/(6)) \end{gathered}`

we get,

`x=r(\frac{\sqrt[]{3}}{2})`
`y=-r((1)/(2))`

Substitute r=-2y in x we get,

`x=-2y(\frac{\sqrt[]{3}}{2})`
`y=-\frac{x}{\sqrt[]{3}}`
`y=-\frac{\sqrt[]{3}x}{3}`

The required rectangular form of the given plar equation is,

`y=-\frac{\sqrt[]{3}x}{3}`