Stop memorizing and start visualizing: how unit circle coordinates define all 6 trig functions.
The Unit Circle Defined
A circle of radius r = 1 centered at the Cartesian coordinate origin (0, 0) with equation x² + y² = 1.
Circle Equation: x² + y² = 1
Connecting Coordinates to Trigonometry
For any angle θ measured counter-clockwise from the positive x-axis, the coordinates of the terminal point on the unit circle are precisely (cos θ, sin θ).
(x, y) = (cos θ, sin θ) | tan θ = y / x = sin θ / cos θ
Degrees to Radians Conversion
Radians represent the arc length traveled along the unit circle circumference (2π radians = 360°).
Conversion: Radians = Degrees × (π / 180°) | Degrees = Radians × (180° / π)
The ASTC All-Positive Quadrant Rule
• Quadrant I (0°–90°): All functions positive (A) • Quadrant II (90°–180°): Sine positive (S) • Quadrant III (180°–270°): Tangent positive (T) • Quadrant IV (270°–360°): Cosine positive (C)
Mnemonic: 'All Students Take Calculus'
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