# sine graph

• Mar 23rd 2006, 02:16 AM
rachael
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?
• Mar 23rd 2006, 06:10 AM
ThePerfectHacker
Quote:

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,
$\displaystyle T(t)=15\sin\left(\frac{\pi t}{12}\right)+20$

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