Temperature Modeling with Sinusoidal Functions

The video tutorial explains how to model the outside temperature over a day using a sinusoidal function. It starts by identifying key temperature points at different times of the day and plotting them. The tutorial then discusses the sine function pattern, including reflections and midline shifts. It calculates the amplitude, period, and phase shift to formulate the final equation for the temperature model. The video concludes with a complete sinusoidal equation that models temperature changes over a 24-hour period.

What is the initial temperature at midnight according to the sinusoidal model?

• 85 degrees

• 56 degrees

• 75 degrees

• 94 degrees

At what time does the temperature first reach its minimum value?

• 6 hours after midnight

• 12 hours after midnight

• 24 hours after midnight

• 18 hours after midnight

What is the pattern of key points in the sinusoidal function described in the video?

• Minimum, Midline, Maximum, Midline, Minimum

• Midline, Minimum, Midline, Maximum, Midline

• Midline, Maximum, Midline, Minimum, Midline

• Maximum, Midline, Minimum, Midline, Maximum

What is the midline value of the sinusoidal function?

• 85

• 94

• 56

• 75

What is the amplitude of the sinusoidal function?

• 19

• 94

• 38

• 75

What is the value of 'a' in the sinusoidal function?

• -75

• 75

• -19

• 19

What is the period of the sinusoidal function?

• 6 hours

• 24 hours

• 18 hours

• 12 hours

What is the value of 'b' in the sinusoidal function?

• 1/6 π

• 1/12 π

• 1/24 π

• 1/18 π

Is there a phase shift in the sinusoidal function?

• Yes, to the right

• No phase shift

• Yes, upward

• Yes, to the left

What is the complete equation for the sinusoidal function modeling the temperature?

• d(t) = -19 cos(1/12 π t) + 75

• d(t) = 19 cos(1/12 π t) + 75

• d(t) = -19 sin(1/12 π t) + 75

• d(t) = 19 sin(1/12 π t) + 75