Question

How do you write the equation using rectangular coordinates given `theta=pi/3`?

Answer 1

`y=sqrt3x`

Explanation:

There are several equalities used to convert between rectangular and polar coordinates. For a list and good explanation as to why they work, see How do you convert rectangular coordinates to polar coordinates?

In this case, as we have no `r` to consider, we will only need

`y/x=tanθ`

Multiplying both sides by `x` gives

`y=xtanθ`

Now substituting `θ=π/3` we get

`y=xtan(π/3)`

`=>y=sqrt3x`

Note that this is as expected, as the polar plot `θ=π/3` takes on all
`r` for values for the angle `π/3`, forming a straight line.