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?
y = a·sin(b·x) + c
c is the value of the midline; c = 70
a is the amplitude (high or low from the midline); a = 10 (found by high - midline)
b is the modification of the period; 360° in a 24 hour day; b = 360/24.