What is the angle between the hour and minute hands at 9 : 45 in the morning?

Correct answer: c π/8 radian

The hour hand is at 9 × 30° + 22.5° = 292.5° and the minute hand at 270°; the gap is 22.5° = π/8.

Why the other options are wrong

• a 0 radian: 0 would need the hands together; at 9 : 45 they are not.
• b π/12 radian: π/12 = 15° comes from taking the hour hand's advance as 15° (half an hour); in 45 minutes it is 22.5°.
• d π/4 radian: π/4 = 45° would need the hour hand at 315°; it is really at 292.5°.