Question

Find an angle in each quadrant with a common reference angle with 310°, from 0°≤θ<360°

a) 310°, 50°, 130°, 230°
b) 50°, 130°, 230°, 310°
c) 50°, 130°, 230°
d) 310°, 50°, 130°

Answer 1

The angles in each quadrant with a common reference angle of 310° are 310°, 50°, 130°, and 230°.

Step-by-step explanation:

The common reference angle for 310° in each quadrant is 50°.

• In the first quadrant, the angle is 310°.
• In the second quadrant, the angle is 180° - 310° = -130°, but since negative angles are not considered in this context, we can consider it as 180° - (-130°) = 180° + 130° = 310°.
• In the third quadrant, the angle is 310° - 180° = 130°.
• In the fourth quadrant, the angle is 360° - 310° = 50°.

Therefore, the angles in each quadrant with a common reference angle of 310° are 310°, 50°, 130°, and 230°.