Question

Convert the equation y =`-(sqrt(3)/(3))x` to polar form?

Answer 1

`theta=(5pi)/6+pin` where `n` is an element of all integers

Explanation:

This is my first time attempting converting from rectangular to polar, so please feel free to correct If I am wrong

The conversion from Rectangular to Polar:
`x=rcostheta`
`y=rsintheta`

And the point is solve for `theta` in this case as the `r` cancels:
1. Substitute into the Rectangular form:
`rsintheta=-sqrt3/3*rcostheta`
2. Subtract `rcostheta` from both sides:
`(rsintheta)/(rcostheta)= -sqrt3/3`
3. Recall `sintheta/costheta= tantheta`:
`tantheta= -sqrt3/3`
4. General solution
`theta=(5pi)/6+pin` where `n` is an element of all integers