<Question>
A figure skater is facing north when she begins to spin to her right. She spins 2250 degrees. Which direction (north, south, east or west) is she facing when she finishes her spin?
</Question>

<think>
<Plan_1>
Okay, let's try to figure out this figure skater problem. So, the skater starts facing north and spins to her right 2250 degrees. We need to find out which direction she's facing after that. Hmm, directions and angles... Right, directions are north, south, east, west, which are basically the four cardinal points. Each of these is 90 degrees apart if you think of a full circle, which is 360 degrees.

<prompt_1.1> Think about how directions relate to degrees in a circle and identify the initial direction. </prompt_1.1>
</Plan_1>

<Execution_1>
<execution_1.1>
So, if she spins 360 degrees, she ends up facing the same direction again, right? But here she's spinning 2250 degrees. That's more than a full rotation. Maybe I need to find out how many full rotations that is and then see the remaining angle.
</execution_1.1>
</Execution_1>

<Plan_2>
Based on execution_1.1:
Wait, 2250 divided by 360. Let me calculate that.

<prompt_2.1> Divide 2250 degrees by 360 to find the number of full rotations and the remaining angle. </prompt_2.1>
</Plan_2>

<Execution_2>
<execution_2.1>
360 times 6 is 2160. 2250 minus 2160 is 90. So that's 6 full rotations (which don't affect the direction) plus 90 degrees. So the remaining angle is 90 degrees.
</execution_2.1>
</Execution_2>

<Plan_3>
Based on execution_2.1:
Now, the key is to figure out which direction she faces after a 90-degree turn to her right from north. But wait, when you spin to the right (clockwise), the directions change in a clockwise order.
So starting from north, turning right (clockwise) 90 degrees would face her east. Another 90 degrees (total 180) would face south, then another 90 (270) would face west, and 360 brings her back to north.

But here, she only turns 90 degrees after the full rotations.

<prompt_3.1> Determine the direction after a 90-degree turn to the right from north. </prompt_3.1>
</Plan_3>

<Execution_3>
<execution_3.1>
So, if she spins 90 degrees to her right from north, she should be facing east. But wait, let me confirm.

Wait, another way to think: directions in terms of standard positions in math. North is 0 degrees or 360, right? Then, each direction is 90 degrees apart. But when you turn right (clockwise), the angle increases in the clockwise direction. So, starting at 0 degrees (north), turning 90 degrees clockwise would be 90 degrees, which is east. Turning another 90 would be 180, which is south, etc.
</execution_3.1>
</Execution_3>

<Plan_4>
Based on execution_3.1:
But in this case, the total rotation is 2250 degrees. So, since each full rotation is 360, subtracting 6*360=2160, 2250-2160=90. So, 90 degrees clockwise from north is east.

But hold on, maybe I need to consider the direction of spin. The problem says she spins to her right. So, if you're spinning to your right, that's a clockwise rotation from your perspective.

<prompt_4.1> Confirm the direction after a 90-degree clockwise turn from north. </prompt_4.1>

Wait, but let me check again. Maybe there's a different way. Let's think of the total degrees.

<prompt_4.2> Re-evaluate the total degrees spun and confirm the remaining angle after full rotations. </prompt_4.2>

So, after 6 full rotations (2160 degrees), she's back to north, then spins another 90 degrees to her right. So from north, turning right (clockwise) 90 degrees is east.

But wait, maybe there's a mistake here. Let me visualize.

<prompt_4.3> Visualize the spin and confirm the final direction. </prompt_4.3>

But wait, another way: let's model the directions as angles. Let's say north is 0 degrees.

<prompt_4.4> Model the directions as angles and confirm the final direction using modular arithmetic. </prompt_4.4>
</Plan_4>

<Execution_4>
<execution_4.1>
But from the skater's perspective, spinning to her right would be clockwise, yes. So, if she's facing north and spins 90 degrees clockwise, she would face east. So, that seems correct.

But wait, another thought: sometimes, in some problems, a right turn could be interpreted as a counter-clockwise rotation? Wait, no. If you're facing north and turn right, your body rotates clockwise. So, the direction you're facing moves clockwise. So, yes, 90 degrees to the right from north is east.

But let me confirm with another example. If she spun 180 degrees to her right, that would be a half rotation clockwise, ending up facing south. Which is correct.
</execution_4.1>

<execution_4.2>
2250 degrees. Since a full rotation is 360, we can compute 2250 modulo 360 to find the equivalent angle within a single rotation. Let's compute that:

2250 divided by 360: 360*6=2160, 2250-2160=90. So 2250 ≡ 90 mod 360. So, effectively, she spins 90 degrees clockwise from north.
</execution_4.2>

<execution_4.3>
Imagine she's facing north. Spinning to her right (clockwise) 90 degrees. So, right from north is east. So yes, that's correct. Alternatively, if she spins 180 degrees to her right, she'd be facing south, and 270 degrees to her right would be west. But 90 degrees is east.
</execution_4.3>

<execution_4.4>
Then, each 90 degrees is a quarter turn. But when you turn right (clockwise), the angle increases. So, turning 90 degrees from north (0) would be 90 degrees, which is east. Turning 180 degrees would be south, 270 degrees west, and 360 back to north.

But in this case, the total rotation is 2250 degrees. To find the effective rotation, we can compute 2250 modulo 360. Let's do that. 2250 divided by 360: 360*6=2160, 2250-2160=90. So 2250 ≡ 90 degrees mod 360. So, the effective rotation is 90 degrees clockwise from north, which is east.
</execution_4.4>
</Execution_4>

<Plan_5>
Based on execution_4.1, execution_4.2, execution_4.3, execution_4.4:
Therefore, the answer should be east.

Wait, but let me double-check. Maybe the initial direction is north, and turning right (clockwise) 90 degrees each time.

<prompt_5.1> Double-check the final direction using step-by-step reasoning. </prompt_5.1>
</Plan_5>

<Execution_5>
<execution_5.1>
So, 2250 degrees is 5*450, but that's not helpful. Alternatively, 2250 divided by 90 is 25. So 25 quarter turns to the right. Each quarter turn is 90 degrees. Starting at north, each right turn moves 90 degrees clockwise.

So, every 4 right turns would be 360 degrees, which brings her back to north. So, 25 right turns. Let's divide 25 by 4. 25 divided by 4 is 6 with a remainder of 1. So, 6 full circles (24 turns) bringing her back to north, and 1 more right turn. So, one right turn from north is east. Therefore, same result.

So, all methods point to east.
</execution_5.1>
</Execution_5>

<Final_answer>
Therefore, the figure skater is facing $\boxed{\text{east}}$ after spinning 2250 degrees to her right.
</Final_answer>
</think>