Geometry

Question Analysis  

Identify the Quadrant I angle corresponding to symmetric unit circle coordinates , focusing on 45-45-90 triangle properties.  

 

Key Concept Explanation  

45-45-90 Triangle: In this isosceles right triangle, both legs are equal, and the hypotenuse is times the leg length.  

On the unit circle, the legs (x and y coordinates) are equal and rationalized to .  

 

Step-by-Step Solution  

1. Recognize symmetric coordinates:  

Equal x and y values () indicate an angle where .  

2. Recall special angles:  

is the only angle in QI with equal sine and cosine values.  

.  

 

Option Analysis

30°: Incorrect ()

45°: Correct (

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