Quadrantal Angle

High School

Definition

Angle in the standard position with a terminal side that lies on the x-axis or y-axis. This means that the angle will be multiples of 90°. Examples include 0°, 270°, -90° and so forth.

Worked examples

\(0^\circ, 90^\circ, 180^\circ, 270^\circ, 360^\circ\)

Each terminal side lies exactly on an axis — these are the basic quadrantal angles.

\(-90^\circ, -180^\circ, 450^\circ, 540^\circ\)

Negative rotations and angles beyond one full turn are also quadrantal if they land on an axis.

\(\frac{\pi}{2}, \pi, \frac{3\pi}{2}, 2\pi\)

In radians, quadrantal angles are multiples of \(\frac{\pi}{2}\).

Common mistakes

\(45^\circ\) is quadrantal → \(45^\circ\) is not quadrantal; only \(0^\circ, 90^\circ, 180^\circ, 270^\circ, \ldots\) are Quadrantal angles must be multiples of 90°, not just any angle in standard position.
\(\sin(90^\circ)\) is undefined because it is quadrantal → \(\sin(90^\circ) = 1\); only some trig functions are undefined at some quadrantal angles Quadrantal does not mean undefined — check each function individually (e.g., tan 90° is undefined, sin 90° is not).
\(360^\circ\) is not quadrantal because it is a full rotation → \(360^\circ\) is quadrantal; its terminal side lies on the positive x-axis Any multiple of 90° qualifies, including full rotations and beyond.

Where you'll use it next

You'll use quadrantal angles when evaluating trigonometric functions, simplifying exact values on the unit circle, and solving trig equations in precalculus and calculus.

Found in 1 StudyPug lesson

Angle in standard position

Grade 12 Math

12th Grade12th