Question

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.

Answer 1

Answer:

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°

Answer 2

Consider D(t) to be the temperature in Fahrenheit at time t, where t is measured in hours since midnight.  

• 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

D(9)    = 20cos [-2π/3] + 85

D(9)    = -20 x 1/2 + 85

D(9)    = 75° F

Therefore ,The temperature at 9 Am to the nearest degree is 75° F.

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