Greenhouse temperature over successive days

The temperature inside a greenhouse is \(16^\circ\mathrm{C}\) at its daily minimum at 5 am on 18 August 2026. It next reaches a minimum at 5 am on 19 August. The average temperature is \(22^\circ\mathrm{C}\).

Let \(t\) be the number of hours after midnight on 18 August 2026. The temperature \(T(t)\), in degrees Celsius, is modelled by \(T(t)=a\cos\bigl(b(t-c)\bigr)+22\), where \(a\), \(b\) and \(c\) are positive constants.

1. Find \(a\) and \(b\).[4]
2. Find the smallest positive value of \(c\).[1]
3. Hence, find the first time on 20 August 2026 at which the model predicts a temperature of \(25^\circ\mathrm{C}\).[4]