Sign Patterns in Quadrants

Trigonometry · Axiom Academy

LESSON Sign Patterns in Quadrants Master the ASTC rule: A simple mnemonic to remember where sine, cosine, and tangent are positive across all four quadrants. The coordinate plane is divided into four quadrants, numbered counterclockwise starting from the upper right. Each quadrant has different sign combinations for x and y coordinates. Quadrant I: x > 0, y > 0 (both positive) Quadrant III: x < 0, y < 0 (both negative) "All Students Take Calculus" tells us which trig functions are positive in each quadrant, starting from Quadrant I and moving counterclockwise. The sign patterns come from the unit circle definitions of sine and cosine. Remember: sin(θ) = y and cos(θ) = x on the unit circle, while tan(θ) = y/x . Sine depends on y → positive when y > 0 (QI & QII) Cosine depends on x → positive when x > 0 (QI & QIV) Tangent is y/x → positive when both have same sign (QI & QIII) Here's the complete ASTC pattern showing all positive and negative signs for sine, cosine, and tangent in each quadrant. This is your go-to reference!

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