Geometry

Question Analysis  

The task is to determine the unit circle coordinates at 60° by applying 30-60-90 triangle ratios in Quadrant I.  

 

Key Concept Explanation  

30-60-90 Triangle: Sides are in the ratio , with 60° opposite the longer leg ().  

 

Step-by-Step Solution  

1. Recall 30-60-90 ratios:  

Opposite 60°: , Adjacent: , Hypotenuse: .  

2. Scale to unit circle:  

Divide by 2: Adjacent = , Opposite = .  

3. Assign coordinates:  

.  

 

Common Mistakes  

Ratio Confusion: Mixing 60° with 30° (60° has a larger y-coordinate).  

Scaling Error: Neglecting to divide by the hypotenuse (2) for unit circle adaptation.  

 

Summary  

The coordinates at 60° on the unit circle are , derived from scaling a 30-60-90 triangle to radius 1.  

Problem-Solving Tips:  

Remember: 60° corresponds to the longer leg (

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