How can coterminal angles be found?

Coterminal angles are angles that share the same terminal side when drawn in standard position, meaning they differ by full rotations. To find coterminal angles, you add or subtract full rotations from the angle in question. Since a full rotation in degrees is 360 degrees, or equivalently, in radians is (2\pi), the correct method to obtain coterminal angles is to add or subtract (360) degrees or (2\pi) radians from the angle.

For example, if you have an angle of (30) degrees, you can find a coterminal angle by calculating (30 + 360n) for any integer (n). Thus, (30 + 360 = 390) degrees is a coterminal angle. Similarly, (30 - 360 = -330) degrees would also yield a coterminal angle.

The other options only suggest adding or subtracting specific angles like (90), (180), or (45) degrees, which do not generally result in angles that are coterminal. They may yield related or supplementary angles but not the same terminal side. Hence, they cannot be used to systematically find all coterminal angles for