Problem
b. A person with a wellbeing index of 6 or higher is Determine the percentage of the 4-week cycle for which the model prean 4. WE7 During one day in October the temperature $T^{\circ} \mathrm{C}$ is given by $T=19-3$ in $\left(\frac{\pi}{12}\right.$ in hours after midnight. a. Calculate the temperature at midnight. b. Determine the maximum temperature during the day and at what time it occurred. c. Calculate the interval over which the temperature varied that day. d. State the period and sketch the graph of the temperature for $t \in[0,24]$. e. If the temperature was below $k$ degrees for 3 hours, obtain the value of $k$ to 1 decimal place.
Solution
Step 1 ：Substitute \(t = 0\) into the given equation \(T = 19 - 3\sin\left(\frac{\pi t}{12}\right)\).
Step 2 ：Solve for \(T\) to find the temperature at midnight.
Step 3 ：Final Answer: The temperature at midnight is \(\boxed{19^\circ C}\).
