Geometry

Question Analysis  

The task is to find an angle with the same cscθ as 30° by leveraging the reciprocal relationship between cscθ and sinθ, focusing on angles in quadrants where sinθ values (and thus cscθ values) are identical.  

 

Key Concept Explanation  

Cosecant Definition: , so angles with the same sinθ have the same cscθ.  

Sine Symmetry: Sinθ is positive in QI and QII. For a QI angle (30°), the corresponding QII angle with the same sine is .  

 

Step-by-Step Solution  

1. Reference Angle for 30°:  

Reference angle = 30° (QI).  

2. Find QII Angle:  

QII angle = .  

3. Verify Sine Values:  

,  

Thus, .  

 

Option Analysis  

210°: Incorrect (QIII,