Final answer:
The closest positive coterminal angle to 32° is 392°, and the closest negative coterminal angle is -328°. These are determined by adding or subtracting 360° to the original angle.
Step-by-step explanation:
To find the closest positive angle and the closest negative angle that is coterminal to 32°, we need to understand that coterminal angles are angles that share the same terminal side but may differ by full rotations of 360°.
The closest positive coterminal angle to 32° is 392°, and the closest negative coterminal angle is -328°. These are determined by adding or subtracting 360° to the original angle.
To find the closest positive coterminal angle to 32°, you can add 360° to 32°:
- 32° + 360° = 392°
This means 392° is the closest positive coterminal angle to 32°.
To find the closest negative coterminal angle, you can subtract 360° from 32°:
- 32° - 360° = -328°
Thus, -328° is the closest negative coterminal angle to 32°.