Step 1 :Find the distance from the origin (r) using the formula r = \(\sqrt{x^2 + y^2}\): \(r = \sqrt{(-3)^2 + 6^2} = \sqrt{9 + 36} = \sqrt{45}\)
Step 2 :Find the angle (θ) using the formula θ = arctan(y/x): \(\theta = \arctan\left(\frac{6}{-3}\right) = \arctan(-2)\)
Step 3 :Since the point is in the second quadrant, add π to the angle: \(\theta = \arctan(-2) + \pi\)
Step 4 :The polar coordinates for the Cartesian coordinate (-3, 6) are: \(r = \sqrt{45}\) and \(\theta = \arctan(-2) + \pi\)
Step 5 :\(\boxed{r = \sqrt{45}, \theta = \arctan(-2) + \pi}\)