Geometry

Question Analysis  

Determine the unit circle coordinates for , leveraging 45-45-90 triangle ratios.  

 

Key Concept Explanation  

45-45-90 Triangle: Sides are in the ratio .  

On the unit circle (hypotenuse = 1), both legs (x and y coordinates) are equal and scaled by .  

 

Step-by-Step Solution  

1. Scale triangle sides to the unit circle:  

Original hypotenuse =  → scale factor = .  

x-coordinate = .  

y-coordinate = .  

2. Coordinates: .  

 

Common Mistakes  

Forgetting to rationalize  to

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