Coterminal angles

Coterminal angles are angles in standard position that share the same terminal side. An angle with measurement $x°$ is coterminal with any angle that can be represented as $x° + 360n$, where $n$ is an integer representing the number of full rotations.

To find a positive coterminal angle for $75°$, add $360°$: $75° + 360° = 435°$. To find a negative one, subtract $360°$: $75° 360° = 285°$. For an angle like $480°$, you can find a smaller positive coterminal angle by subtracting $360°$: $480° 360° = 120°$.

Think of coterminal angles like a race car on a circular track. Finishing one lap, or even spinning out backward, puts you right back at the starting line. These angles land in the exact same spot, they just took a different number of spins to get there! To find an angle's buddy, just add or subtract a full 360° circle.