Chapter 8.3

ASTC rule in trigonometry (All Students Take Calculus)

What You'll Learn

Identify which trigonometric ratios are positive in each quadrant
Apply the ASTC rule using the mnemonic 'Add Sugar To Coffee'
Determine sign conventions for sine, cosine, and tangent across all four quadrants
Recognize that all trig ratios are positive in quadrant I, and only one in each of II, III, and IV

What You'll Practice

1

Memorizing which ratio is positive in each quadrant using ASTC

2

Determining the sign of sine, cosine, and tangent for angles in different quadrants

3

Applying the 'Add Sugar To Coffee' mnemonic to recall quadrant rules

Why This Matters

The ASTC rule is essential for solving trigonometric equations and evaluating trig functions at any angle. You'll use this quadrant sign convention constantly in precalculus, calculus, physics, and engineering to correctly determine positive and negative values.

Before You Start — Make Sure You Can:

Use sine ratio to calculate angles and sides (Sin = \( \frac{o}{h}\) )Use cosine ratio to calculate angles and sides (Cos = \( \frac{a}{h}\) )Use tangent ratio to calculate angles and sides (Tan = \( \frac{o}{a}\) )

This Unit Includes

1 Video lesson
Practice exercises
Learning resources

Skills

ASTC Rule
Trigonometry
Quadrants
Unit Circle
Sine
Cosine
Tangent
Sign Convention
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