Okay, so I need to convert the rectangular coordinate (0,3) to polar coordinates. Hmm, let me think. Polar coordinates are represented as (r, θ), where r is the radius and θ is the angle. Right, so first, I remember that the formulas to convert from rectangular (x, y) to polar coordinates are r = √(x² + y²) and θ = arctan(y/x). But wait, arctan(y/x) might not always give the correct angle, especially when x is zero or negative. Let me make sure I handle that correctly.

First, let's compute r. Since the rectangular coordinates are (0,3), that means x is 0 and y is 3. Plugging into the formula for r: r = √(0² + 3²) = √(0 + 9) = √9 = 3. Okay, so r is 3. That part seems straightforward.

Now, θ. Since x is 0, the angle θ is going to be either π/2 or 3π/2, right? Because when x is 0, the point lies on the y-axis. But since y is positive (3), the point is above the origin on the positive y-axis. So θ should be π/2. Let me confirm that with the arctan formula. If x is 0, then arctan(y/x) becomes arctan(3/0). Hmm, 3 divided by 0 is undefined, but in the limit as x approaches 0 from the positive side, arctan approaches π/2. However, if x is exactly 0, then we have to consider the quadrant. Since x is 0 and y is positive, the angle is directly upwards along the y-axis, which is π/2 radians. So θ should be π/2. 

Wait, but sometimes when x is 0, people use the sign of y to determine θ. If y is positive, θ is π/2; if y is negative, θ is 3π/2. In this case, y is positive, so θ is π/2. That makes sense. 

Let me check with the unit circle. On the unit circle, (0,1) corresponds to θ = π/2, and (0,-1) is θ = 3π/2. Our point is (0,3), which is 3 units up along the y-axis, but the angle is still the same as (0,1) because direction is what matters. So θ is indeed π/2. 

Therefore, putting it all together, the polar coordinates should be (3, π/2). Let me just recap to make sure I didn't miss anything. The radius is the distance from the origin, which is 3. The angle is the angle made with the positive x-axis. Since the point is on the positive y-axis, that's π/2. Yep, that seems right. 

I don't think there's any ambiguity here because the point isn't in any other quadrant. If the x were negative, we'd have to adjust the angle accordingly, but since x is 0 here, it's straightforward. So I think this is the correct conversion.
Therefore, converting the rectangular coordinates $(0, 3)$ to polar coordinates, we have $r = 3$ and $\theta = \frac{\pi}{2}$.
</think>