Final answer:
Coterminal angles share the same terminal side and adding or subtracting multiples of 360° or 2π radians find them. For each angle given, there are coterminal angles that can be found by this rule, such as 640° and -80° for 280° or angles less than 2π radians for c. 50π/9 and d. 14π/9.
Step-by-step explanation:
To determine which angles are coterminal with a given angle, we need to add or subtract multiples of 360° (or 2π radians) to the original angle. Coterminal angles are those that share the same terminal side when drawn in standard position on a coordinate plane. The original question seems to be missing the angle with which we're supposed to find coterminal angles, so I will assume that we need to find angles coterminal with each option provided (280°, -440°, 50π/9 radians, 14π/9 radians).
- To find an angle coterminal with 280°, we can add 360° to get 640° or subtract 360° to get -80°. Both are coterminal with 280°.
- For an angle coterminal with -440°, adding 360° gives us -80°, which is coterminal with -440°.
- To find angles coterminal with 50π/9 radians, we can add or subtract multiples of 2π radians. Since 2π is approximately 6.2832 (50π/9 is roughly 17.45), we can subtract 6.2832 to find an angle less than 2π that is coterminal.
- For an angle coterminal with 14π/9 radians, we can also add or subtract 2π to find coterminal angles. 14π/9 is approximately 4.8869, so adding 2π gives us an angle just over 2π that is coterminal.