not quite sure how an equation would help you out on this due to the rotation... the only thing i can think of is calculating the arc of the circle as arcLength = ThetaAngle * Radius. And constantly update your max radius of the ship by 1 coordinate, so it would scan based on the cented of the ship, but to fix that use MaxRadius - InitialRadius(ship). after each update you scan the arch coordinates to see if they collide with the enemy ship.
That could work... if I understand correctly what you are trying to do. If the arc rotates with the ship im not sure how the equation will work with the different signs.