quadrant

(noun)

One of the four quarters of the Cartesian plane bounded by the xxx-axis and yyy-axis.

Related Terms

  • -axis
  • y-axis
  • x-axis
  • ndependent and Dependent Variables
  • dependent variable
  • independent variable
  • ordered pair

Examples of quadrant in the following topics:

  • Special Angles

    • In quadrant II, “Smart,” only sine is positive.
    • Reference angles in quadrant I are used to identify which value any angle in quadrants II, III, or IV will take.
    • For any given angle in the first quadrant, there is an angle in the second quadrant with the same sine value.
    • For any angle in quadrants II, III, or IV, there is a reference angle in quadrant I.
    • For any angle in quadrants II, III, or IV, there is a reference angle in quadrant I.
  • The Cartesian System

    • The Cartesian coordinate system is broken into four quadrants by the two axes.
    • Some basic rules about these quadrants can be helpful for quickly plotting points:
    • Quadrant II: Points have negative xxx and positive yyy coordinates, (−x,y)(-x,y)(−x,y).
    • Quadrant IV: Points have positive xxx and negative yyy coordinates, (x,−y)(x,-y)(x,−y).
    • The four quadrants of theCartesian coordinate system.
  • Defining Trigonometric Functions on the Unit Circle

    • The x- and y-axes divide the coordinate plane (and the unit circle, since it is centered at the origin) into four quarters called quadrants.
    • We label these quadrants to mimic the direction a positive angle would sweep.
    • The four quadrants are labeled I, II, III, and IV.
  • Sine and Cosine as Functions

    • Notice how the sine values are positive between 000 and π\piπ, which correspond to the values of the sine function in quadrants I and II on the unit circle, and the sine values are negative between π\piπ and 2π2\pi2π, which correspond to the values of the sine function in quadrants III and IV on the unit circle.
  • Double and Half Angle Formulae

    • Recall that different signs are applied to trigonometric functions that fall in each of the four quadrants (according to the mnemonic rule "A Smart Trig Class").
    • Notice that we used only the positive root because 15∘15^{\circ}15​∘​​ falls in the first quadrant and sin(15∘)\sin(15^{\circ})sin(15​∘​​) is therefore positive.
  • Pythagorean Identities

    • If we know the quadrant where the angle is, we can easily choose the correct solution.
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