Outside temperatures over the course of a day can be modeled as a sinusoidal function. Suppose the high temperature of105°Foccurs at 5PM and the average temperature for the day is85°F. Find the temperature, to the nearest degree, at 9AM.

The temperature at 9AM = 75°F

Step-by-step explanation:

Consider D (t) be the temperature in Fahrenheit at time t, where t is measured in hours since midnight. It knows when the maximum temperature occurs. Then it can create a model using a cosine curve.

Vertical shift, D = 85°F

Amplitude, A = (105-85) °F = 20°F

Horizontal stretch factor, B = 2π/24 = π/12

Horizontal shift = - (12+5) = - 17

Using the information, we have this model

D (t) = 20cos [π/12 (t-17) ] + 85

D (9) = 20cos [π/12 (9-17) ] + 85

= 20cos [-2π/3] + 85

= - 20 x 1/2 + 85

= 75°