First, good job finding r = sqrt(27 + 9) and z = -5. To find theta simply, try drawing a picture of the x-y (or r-theta) plane. This should look like a familiar triangle: a right triangle made by half an equilateral, which confirms your "variation of 30 degrees" (though you'll want to put that into radians). To confirm this conversion, use the following equations: $x = rsin\theta, y = rcos\theta \implies tan\theta = \frac{rsin\theta}{rcos\theta} \implies \theta = arctan\left(\frac{x}{y}\right)$ Keep in mind that tan(theta) = tan(theta + pi), so check theta against x and y for reasonableness.