Geometry

Question Analysis  

The task is to find the unit circle coordinates for  (210°) by relating it to Quadrant I’s 30° (π/6) ratio and adjusting signs for Quadrant III using reference angles.  

 

Key Concept Explanation  

Reference Angle:  lies in Quadrant III. Its reference angle is  (30°).  

Trig Signs in QIII: Both cosine (x) and sine (y) are negative (ASTC: Tan (+), so Sin/Cos (-)).  

 

Step-by-Step Solution  

1. Identify the reference angle:  

Reference angle =  (30°).  

2. Apply Quadrant I ratios for 30°:  

, .  

3. Adjust signs for Quadrant III:  

,  

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