Geometry

Question Analysis  

The question asks which trigonometric value is positive in Quadrant II, focusing on the sign conventions of trig functions across quadrants.  

Key Concept Explanation  

In the coordinate plane:  

Quadrant I: All trig functions (+).  

Quadrant II: Sin (+), Cos (-), Tan (-).  

Quadrant III: Tan (+), Sin (-), Cos (-).  

Quadrant IV: Cos (+), Sin (-), Tan (-).  

Memory aid: ASTC (All Students Take Calculus) for positive functions per quadrant.  

 

Step-by-Step Solution  

1. Recall the sign of each trig function in Quadrant II:  

Sin: Positive (y-coordinate is positive).  

Cos: Negative (x-coordinate is negative).  

Tan (): Negative (positive ÷ negative = negative).  

 

Option Analysis  

Sin: Correct (positive in Quadrant II).  

Cos: Incorrect (negative).  

Tan: Incorrect (negative).  

None of the above: Incorrect (Sin is positive).  

 

Common Mistakes  

Forgetting the ASTC rule or misassigning signs to coordinates.  

Confusing Tan’s sign (depends on both Sin and Cos).  

 

Summary  

In Quadrant II, Sin is the only positive trigonometric value.  

Problem-Solving Tips: 

Use ASTC to memorize signs: A (I), S (II), T (III),...