Coterminal Angles

Definition

Coterminal angles share the same terminal side after differing by one or more full rotations.

Why It Matters

They show that while our ‘names’ for things might differ, the underlying physical state and terminal direction remain the same.

Core Concepts

• In degrees, coterminal angles have form $\theta+360^\circ k$; in radians, $\theta+2\pi k$, where $k\in\mathbb{Z}$.
  • How to read: “The angle theta plus three hundred sixty degrees times k, or theta plus two pi k, where k is any integer.”
  • Meaning / when to use: Add or subtract full rotations to rewrite any angle into standard interval $Periodic Functions
• Trigonometric Functions