Answer:
a) the trigonometric function is;

b)
( to two decimal places)
Step-by-step explanation:
This data can be represented by the sinusoidal function of the form :

where A = amplitude and which can be determined via the formula:



A = 7.5° C
where B = the frequency;
Since the data covers a period of 3 days ; then 
( where 365 is the time period )
The vertical shift is found by the equation D;
D = 
D = 
D = 21.5
Replacing the values of A ; B and D into the above sinusoidal function; we have :

From the question; when it is 7th of the year ( i.e January 7);
t = 7 and the temperature (y) = 29° C
replacing that too into the above equation; we have:









Thus; the trigonometric function is;

Similarly; to determine the temperature o Jan 31; i.e when t= 31 ; we have :






( to two decimal places)