Geometry

Question Analysis  

Determine the x-coordinate of a unit circle point in Quadrant I with , focusing on axis-aligned angles.  

 

Key Concept Explanation  

Unit Circle Equation: .  

Axis Angles: The point lies on the positive y-axis (), where .  

 

Step-by-Step Solution  

1. Apply the unit circle equation:  

.  

2. Simplify:  

.  

3. Solve for :  

  (only solution, as Quadrant I does not restrict x here—it is uniquely determined by ).  

 

Common Mistakes  

Forgetting that uniquely defines on the unit circle.  

 

Summary  

The x-coordinate is .  

Problem-Solving Tips:  

Remember: On the unit circle,

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