Question

How do you convert `y = (sqrt(3)/3)x` into polar form?

Answer 1

`tan theta=sqrt3/3`

Explanation:

Start from the given `y=sqrt3/3*x`

from the conversion equivalents

`y=r*sin theta`

`x=r*cos theta`

Replace now the variables `x` and `y` with the equivalent expressions in terms of `r` and `theta`

`y=sqrt3/3*x`

`r*sin theta=sqrt3/3*r*cos theta`

`r*sin theta=sqrt3/3*r*cos theta`

Dividing both sides by `r*cos theta`

`(r*sin theta)/(r*cos theta)=(sqrt3/3*r*cos theta)/(r*cos theta)`

`(cancelr*sin theta)/(cancelr*cos theta)=(sqrt3/3*cancel(r*cos theta))/(cancel(r*cos theta))`

`tan theta=sqrt3/3`

Have a nice day !!! from the Philippines...