Quadrants

High School

Definition

From the greek origin meaning 4. In plane geometry quadrants refers to the 4 different sections of a graph divided by X and Y axis. Imagine a square being cut evenly into 4 pieces, 2 at the top and 2 at the bottom. The 4 sections are usually numbered from 1-4, with the top right being quadrant 1, and naming counterclockwise, quadrant 2 on the top left, quadrant three at bottom left and quadrant 4 on the bottom right. We can use a mnemonic to help us remember which of three trigonometry functions are positive in which quadrant. "All Science Teachers Crazy" is placed in order of the quadrants. All represents all three functions are positive, Science represents Sin being positive in its quadrant, Teachers represents Tan, and Crazy represents Cos.

Worked examples

\((3, 2)\) is in Quadrant I; \((-4, 5)\) is in Quadrant II; \((-1, -3)\) is in Quadrant III; \((6, -2)\) is in Quadrant IV

The signs of the x and y coordinates tell you which quadrant: I is (+,+), II is (−,+), III is (−,−), IV is (+,−).

\(\sin(120^\circ) > 0\) because \(120^\circ\) is in Quadrant II, where sine is positive ("Science")

Use "All Science Teachers Crazy" counterclockwise from QI to remember which trig functions stay positive in each quadrant.

Common mistakes

numbering clockwise: calling the bottom-right Quadrant II → numbering counterclockwise: Quadrant I (top-right), II (top-left), III (bottom-left), IV (bottom-right) Quadrants are always numbered counterclockwise starting from the top right.
\((0, 5)\) is in Quadrant I or II → \((0, 5)\) lies on the positive y-axis, not in any quadrant Points on either axis are not inside a quadrant.
cosine is positive in Quadrant II because "Science" is there → only sine is positive in Quadrant II ("Science"); cosine is negative Each letter in "All Science Teachers Crazy" tells which function is positive: S=sine, T=tangent, C=cosine.

Where you'll use it next

You'll use quadrants to graph lines and curves, identify domains and ranges, solve systems of equations visually, analyze trigonometric functions on the unit circle, and work with polar coordinates in precalculus and calculus.

Found in 1 StudyPug lesson

Mastering the Cartesian Plane: A Complete Guide

Grade 7 Math

Unlock the power of the Cartesian plane with our in-depth guide. Learn to plot points, navigate quadrants, and apply concepts to real-world problems. Perfect for students at all levels.

7th Grade7th