1. ## sine graph

10 The temperature T°C at a town in central Australia at time t hours after 8 am can be modelled by . T(t) = 15 sin [(pit)\12] + 20
a What is the minimum temperature in °C, and at what time of day does it occur?
i do not know how to work out the time of the day. why is the minimum temperature is 5 rather than -5?

2. Originally Posted by rachael
10 The temperature T°C at a town in central Australia at time t hours after 8 am can be modelled by . T(t) = 15 sin [(pit)\12] + 20
a What is the minimum temperature in °C, and at what time of day does it occur?
i do not know how to work out the time of the day. why is the minimum temperature is 5 rather than -5?
The minimum that,
$T(t)=15\sin\left(\frac{\pi t}{12}\right)+20$

gets, is when $\sin\left(\frac{\pi t}{12}\right)$ is minimum. As you know the sine is minimum at -1. Thus, $15(-1)+20=5$ is the minimum value.