Answer
A good approximation for the everage yearly temperature would be $67.5^o\text{ F}$, which is the vertical translation of the fine function in the formula for $f$.
Work Step by Step
A good approximation of the average yearly temperature in San Antonio would be the average of the highest average temperature $(84^o\text{ F}$ and the lowest average temperature ($51^o\text{ F}$., which is:
$$\dfrac{51^o+84^o}{2}=67.5^o\text{ F}$$
Notice that this value is actually the vertical translation of the sine function in the formula for $f$.
