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Quadrants and Signs of Trigonometric Functions


Interactive visualization showing mathematical reasoning behind function signs

Keyboard: Press 1-4 to select quadrants or click the corresponding button
Unit Circle - Quadrant 1(x, y)r+x+y-x-yIIIIIIIV

Quadrant 1 Coordinates

x-coordinate: +
y-coordinate: +
radius (r): always +
Reference angle: 0° to 90° (0 to π/2)

sin(θ) in Quadrant 1

Sign: +
Mathematical Reasoning:
sin θ = y/r. Since y is positive and r is always positive, sin θ is positive.

All Functions in Quadrant 1

sin
+
cos
+
tan
+
csc
+
sec
+
cot
+

Key Concepts

Fundamental Definitions:
• sin θ = y/r, cos θ = x/r, tan θ = y/x
• csc θ = r/y, sec θ = r/x, cot θ = x/y
Memory Aid “ASTC”:
• Quadrant I: All positive
• Quadrant II: Sine positive
• Quadrant III: Tangent positive
• Quadrant IV: Cosine positive