Geometry

Question Analysis  

The task is to determine the unit circle coordinates for 150° using Quadrant I’s 30-60-90 triangle ratios, focusing on angle symmetry and trigonometric sign adjustments for Quadrant II.  

 

Key Concept Explanation  

Reference Angle: 150° lies in Quadrant II. Its reference angle is .  

Trig Signs in QII: Cosine (x-coordinate) is negative, sine (y-coordinate) is positive (ASTC rule: Sin positive in QII).  

 

Step-by-Step Solution  

1. Identify the reference angle:  

Reference angle for 150° is 30°.  

2. Apply Quadrant I ratios to the reference angle:  

In QI, , .  

3. Adjust signs for Quadrant II:  

 (x-negative in QII).  

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