Outside temperatures over the course of a day can be modeled as a sinusoidal function.

Question

Outside temperatures over the course of a day can be modeled as a sinusoidal function. Suppose the temperature varies between 44°F and 60°F during the day and the average daily temperature first occurs at 10 a.m. How many hours after midnight does the temperature first reach 48°F?

Answer 1

Pk, I hope you have done a fair bit of work manipulating the sine function and are comfortable with vertical shifts, changes to amplitude, and changes to period.

If f(x) = sin(x), then the "avg. temperature " would be zero at t = 0, the high temperature would be 1 at t = pi/2, and the low temperature would be -1 at t =3 pi/2---you have to change all this to fit the question.

Take a look at f(x) = a*sin(b*(x - c)) + d and make the necessary changes to "a," "b," and "c," and "d." I hope this helps, but it is hard for me to know how much work you have done with graph of sin(x), and there is no point in me giving you the answer if you haven't worked with manipulating sine functions--please let me know if this helps----Andrew