The angle between the hour hand and the minute hand (the smaller one) can be calculated by the rotation period of the two hands.

The hour hand cycle is t = 12 hours = 720 minutes, and the minute hand cycle is t = 1 hour = 60 minutes.

At zero, the hour hand and the minute hand coincide (the included angle is 0).

From 0: 00 am to 8: 35 am, the time is t = 8: 35 = 5 15 minutes.

During this period, when the clockwise rotation angle θ = ω, * t = (2π/t) * t = 2π t/t.

When θ is = 2π * 5 15/720 radians = 103π/72 radians.

During this period, the minute hand turns eight times and then turns θ minutes = 2π * (7/ 12) radian = 7π/6 radian.

So, the angle between the hour hand and the minute hand at this time is

When θ = θ,-θ minute = (103π/72) radian -(7π/6) radian = 19π/72 radian = (19/72) * 180 degrees = 47.