Determine two coterminal angles (one positive and one negative) for θ = −503°.
a. 217°,− 323°
b. 217°, − 143°
c. 307°, − 413°
d. 127°, − 323°
e. 127°, − 233°
To find two coterminal angles (one positive and one negative) for θ = -503°, we need to add or subtract one full revolution (360°) until we obtain angles in the desired range.
1. To find the positive coterminal angle, we add 360° to -503°:
-503° + 360° = -143°
2. To find the negative coterminal angle, we subtract 360° from -503°:
-503° - 360° = -863°
Comparing these results with the given options:
a. 217°,− 323°
b. 217°, − 143° (Correct)
c. 307°, − 413°
d. 127°, − 323°
e. 127°, − 233°
The correct answer is b. 217°, − 143°.