Angles in Four Quadrants

Trigonometry · Axiom Academy

LESSON Angles in Four Quadrants Understanding how angles in different quadrants relate to reference angles, and how to use them to determine coordinates on the unit circle. The coordinate plane is divided into four quadrants by the x and y axes. As an angle rotates counterclockwise from the positive x-axis, it passes through all four quadrants: No matter which quadrant an angle is in, its reference angle is always between 0° and 90°. The reference angle tells us the "base" angle that we're working with, regardless of direction. The formula for finding a reference angle depends on which quadrant the angle is in: 4. Using Reference Angles for Coordinates On the unit circle, any angle's coordinates (x, y) can be found using its reference angle. The reference angle gives us the magnitude, while the quadrant determines the signs: Example: For an angle of 150° in Quadrant II: Reference angle = 180° - 150° = 30° In Quadrant II: x is negative, y is positive A helpful way to remember which trigonometric functions are positive in each quadrant is the ASTC rule : "All Students Take Calculus"

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