Geometry

Question Analysis  

The task is to find an angle with the same secθ as 45° by analyzing the relationship between secant and cosine, focusing on quadrants where cosine values (and thus secant values) are identical.  

 

Key Concept Explanation  

Secant Definition: , so angles with the same cosθ have the same secθ.  

Cosine Symmetry: Cosθ is positive in QI and QIV. For a QI angle (45°), the corresponding QIV angle with the same cosine is .  

 

Step-by-Step Solution  

1. Reference Angle for 45°:  

Reference angle = 45° (QI).  

2. Find QIV Angle:  

QIV angle = .  

3. Verify Cosine Values:  

,  

Thus,

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