Geometry

Question Analysis

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

Key Concept Explanation

Using the ASTC rule for sign patterns:

Quadrant I: All (+)

Quadrant II: Sin (+)

Quadrant III: Tan (+)

Quadrant IV: Cos (+)

Mnemonic: All Students Take Calculus (indicates positive functions per quadrant).

Step-by-Step Solution

1. Recall coordinates in Quadrant III:

x < 0, y < 0 (both negative), and r > 0 always.

2. Relate to trig functions:

Sin = (negative, y < 0).

Cos = (negative, x < 0).

Tan =

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