Question

.Over a 24-hour period, the temperature in a town can be modeled by one period of a sinusoidal function. The temperature measures 70°F in the morning, rises to a high of 80°F, falls to a low of 60°F, and then rises to 70°F by the next morning.

What is the equation for the sine function f(x), where x represents time in hours since the beginning of the 24-hour period, that models the situation?

Answer 1

70 is the midpoint (average of high and low), so we will have
f(x) = 70+asin(kx)
the amplitude is 10, so
f(x) = 70+10sin(kx)
The period is 24 hours, so 2pi/k=24
f(x) = 70+10sin(pi/12 x)