Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high temperature for the day is 100 degrees and the low temperature of 70 degrees occurs at 5 AM. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t. Assume the next low is 24 hours later.

The function for the outside temperature is represented by , where t is measured in hours.

Step-by-step explanation:

Since outside temperature can be modelled as a sinusoidal function, the period is of 24 hours and amplitude of temperature and average temperature are, respectively:

Amplitude

Mean temperature

Given that average temperature occurs six hours after the lowest temperature is registered. The temperature function is expressed as:

Where:

- Mean temperature, measured in degrees.

- Amplitude, measured in degrees.

- Daily period, measured in hours.

- Time, measured in hours. (where t = 0 corresponds with 5 AM).

If , and , the resulting function for the outside temperature is: