Geometry

Question Analysis  

The question asks which angle has the same sin θ as 30°, focusing on identifying angles in different quadrants with identical sine values (same y-coordinate on the unit circle).  

 

Key Concept Explanation  

Sine and Quadrants: Sin θ is positive in QI and QII, negative in QIII and QIV.  

Reference Angles: Angles in QII that share a reference angle with QI have the same sine value. For 30° (QI), the corresponding QII angle is .  

 

Step-by-Step Solution  

1. Identify the reference angle for 30°:  

Reference angle = 30° (already in QI).  

2. Find the QII angle with the same reference angle:  

QII angle = .  

3. Verify sine values:  

,  

.  

 

Option Analysis  

150°: Correct. Lies in QII, the supplement of 30°, same sine value .(Correct)

210°: Incorrect. Lies in QIII,

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