Quadrantal angle

Definition

A quadrantal angle is an angle in standard position whose terminal side lies on one of the coordinate axes. These angles are always multiples of $90^\circ$ or $\frac{\pi}{2}$ radians.

5 Must Know Facts For Your Next Test

1. Quadrantal angles include $0^\circ$, $90^\circ$, $180^\circ$, and $270^\circ$.
2. The sine and cosine values of quadrantal angles are always 0, 1, or -1.
3. At $0^\circ$ (or $0$ radians), $\cos(0) = 1$ and $\sin(0) = 0$.
4. At $90^\circ$ (or $\frac{\pi}{2}$ radians), $\cos(90^\circ) = 0$ and $\sin(90^\circ) = 1$.
5. Quadrantal angles are used to determine reference angles in trigonometry.

Review Questions

• What are the sine and cosine values for the quadrantal angle at $180^{\circ}$?
• Explain why the terminal side of a quadrantal angle lies on a coordinate axis.
• How do you identify a quadrantal angle on the unit circle?

Related terms

Unit Circle: A circle with a radius of one, centered at the origin of a coordinate plane, used to define trigonometric functions.

Standard Position: An angle positioned so its vertex is at the origin and its initial side lies along the positive x-axis.

Terminal Side: The ray that rotates from the initial side to form an angle in standard position.