Geometry

Question Analysis  

The question focuses on identifying an angle with the same secθ as 30° by leveraging the relationship between secant and cosine and analyzing angles across different quadrants.

 

Key Concept Explanation  

Recall that , so angles with the same cosθ value will have the same secθ value. Cosθ is positive in Quadrants I and IV and negative in Quadrants II and III. Angles in Quadrant IV that share a reference angle with those in Quadrant I have identical cosθ values.

 

Step-by-Step Solution  

1. Identify the reference angle for 30°: The reference angle for 30° is 30° itself as it lies in Quadrant I.

2. Find the corresponding angle in Quadrant IV: Calculate . This angle in Quadrant IV has the same reference angle as 30°.

3. Since , then  and .

 

Option Analysis  

210°: Incorrect. Lies in Quadrant III, , so

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