Geometry

Question Analysis  

The question asks in which quadrants tan θ is positive, requiring knowledge of trigonometric sign conventions.  

Key Concept Explanation  

Sign of tan θ: , so it is positive when sin and cos have the same sign (both + or both -).  

ASTC rule:  

Q1: Sin (+), Cos (+) → Tan (+)  

Q2: Sin (+), Cos (-) → Tan (-)  

Q3: Sin (-), Cos (-) → Tan (+)  

Q4: Sin (-), Cos (+) → Tan (-)  

Step-by-Step Solution  

1. Identify quadrants where sin and cos share the same sign:  

Q1: Both + → Tan (+)  

Q3: Both - → Tan (+)  

2. Thus, tan θ is positive in Quadrant I and III.  

Option Analysis  

Quadrant I and II: Q2 has Tan (-)(Incor...