
circular functions
the temperature T °C inside a house at a time t hours after 6.00 am is given by T=184cos(pi t/12) for 0\leqslant t\leqslant 24
the temperature \theta °C outside a house at time t hours after midnight is given by \theta =116cos(pi t/12) for 0\leqslant t\leqslant 24
if the difference between the inside and outside temperatures can be represented by D=T\theta , sketch the graph of D. determine when the difference between inside and the outside temperature is less then 6°C.
guys anyideas?

Yes that you should show some effort yourself first! All you are asked to do is subtract two functions. One thing to be carfule about the variable "t" in the two equations represent two different things. In the formula for "T", t is "hours after 6.00 am" while in the formula for "$\displaystyle \theta$", t is "hours after midnight".
If we call the "t" in the formula for T t' so we can distinguish then t'= t 6 because, of course, 6 am is 6 hours after midnight.

so for function T & theta, you substitute 6 into the equation. which will give you 18 and 11. 6pm and 11am