Question

How do you convert `(theta) = pi/3` into cartesian form?

Answer 1

`y = sqrt(3)x`

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 = tan(theta)`

Multiplying both sides by `x` gives

`y = tan(theta)x`

But substituting `theta = pi/3` we get

`y = tan(pi/3)x`

`=> y = sqrt(3)x`

(Note that this is as expected, as the polar plot `theta = pi/3` takes on all `r` values for the angle `pi/3`, forming a straight line)