Final answer:
The question involves finding coterminal angles by adding or subtracting multiples of 360° to a given angle. An example with 30.1° demonstrates that 390.1°, 750.1°, and -329.9° are all coterminal with the original angle.
Step-by-step explanation:
The student is asking for three angles, one negative and two positive, that are coterminal with a given angle. Coterminal angles are those that share the same initial and terminal sides when graphed in standard position on a coordinate plane but may have different rotations. For a given angle θ, coterminal angles can be found by adding or subtracting multiples of 360° (or 2π radians) for angles measured in degrees, or multiples of 2π (or 360°) for angles measured in radians.
For example, to find angles coterminal with 30.1°, we can add and subtract 360 degrees:
- Positive coterminal angle: 30.1° + 360° = 390.1°
- Another positive coterminal angle: 30.1° + 2×360° = 750.1°
- Negative coterminal angle: 30.1° - 360° = -329.9°
The process is the same for any other angle, regardless of whether it is initially positive or negative.