Understanding Sinusoidal Functions in Temperature Modeling

The video explains how to model the outside temperature over a day using a sinusoidal function. It starts by identifying the high and low temperatures and calculating the midline. Key points are identified, and the period of the function is determined. The video then demonstrates how to plot these points and sketch the sinusoidal graph. It discusses transformations, including reflection, amplitude, and phase shifts, to derive the equation of the function. The final equation models the temperature over a 24-hour period using a cosine function.

What is the high temperature mentioned in the sinusoidal temperature model?

• 100 degrees

• 96 degrees

• 80 degrees

• 64 degrees

At what time does the low temperature of 64 degrees occur?

• Midnight

• 4 A.M.

• Noon

• 8 P.M.

What is the midline of the sinusoidal function based on the given temperatures?

• Y = 64

• Y = 96

• Y = 80

• Y = 100

Which point is NOT part of the sinusoidal function based on the temperature data?

• (12,80)

• (4,64)

• (16,96)

• (28,64)

What is the period of the sinusoidal function representing the temperature?

• 6 hours

• 12 hours

• 24 hours

• 48 hours

Which function is used to model the temperature in this problem?

• Tangent function

• Cosine function

• Exponential function

• Sine function

What is the amplitude of the sinusoidal function?

• 32

• 16

• 64

• 80

How is the graph of the sinusoidal function shifted horizontally?

• Left 8 units

• Right 8 units

• Left 4 units

• Right 4 units

What is the value of B in the sinusoidal function equation?

• π/6

• π/12

• π/24

• 2π

What is the final equation of the sinusoidal function for temperature?

• D(T) = 16 sin(π/12 (T - 4)) + 80

• D(T) = 16 cos(π/12 (T - 4)) + 80

• D(T) = -16 sin(π/12 (T - 4)) + 80

• D(T) = -16 cos(π/12 (T - 4)) + 80