Question

The temperature in a town over 24 hours can be modeled by a trigonometric function. The temperature was 76°F at 12 a.m. and at 12 p.m. The lowest temperature of 70°F occurred at 6 a.m., and the highest temperature of 82°F occurred at 6 p.m. Which function can be used to model the temperature, y, during the time in hours, x?

Answer 1

The temperature in the town can be modeled using a sinusoidal function, such as the sine or cosine function.

Step-by-step explanation:

The temperature in a town over 24 hours can be modeled by a sinusoidal function. In this case, we can use the sine or cosine function to model the temperature changes throughout the day. Since the temperature was 76°F at 12 a.m. and 12 p.m., we can set the midline of the function as y = 76. The amplitude is half the difference between the highest and lowest temperatures, which is (82-70)/2 = 6°F. The period of the function is 24 hours, so we can use the equation:

y = 6*sin((π/12)*(x-6))+76

This equation represents the temperature, y, at a given time, x, in hours.