Geometry

Question Analysis  

The question aims to find an angle with the same cscθ as 60°, leveraging the reciprocal relationship between cscθ and sinθ and analyzing angles across different quadrants.

 

Key Concept Explanation  

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

 

Step-by-Step Solution  

1. Identify the reference angle for 60°: The reference angle for 60° is 60° itself as it lies in Quadrant I.

2. Find the corresponding angle in Quadrant II: Calculate . This angle in Quadrant II has the same reference angle as 60°.

3. Since , then  and .

 

Option Analysis  

150°: Incorrect. Its reference angle is 30°, and , so

Click "Show Answer" to reveal the answer and analysis