Sinusoidal Function Context and Data Modeling Practice Set 1 (DR

1. The figure at right shows the number of hours of daylight in St. Augustine, Florida. Hours of daylight are at a minimum of 10 hours in December. Hours of daylight are at a maximum of 14 hours in June. Let x represent the month of the year, where Jan. =1, Feb. = 2, and Dec. = 12. If y represents the number of hours of daylight in month x, use a sine function in the form y = A sin[B(x – C)] + D to model the hours of daylight. Explain the meaning of the points of inflection in context to the scenario.

• The points of inflection represent the months where the rate of change of daylight hours is greatest.

• The points of inflection represent the months with the least daylight hours.

• The points of inflection represent the months with the most daylight hours.

• The points of inflection have no specific meaning in this context.

The London Eye Ferris wheel has a diameter of 135 meters. A ride on the Eye will complete one rotation every 30 minutes. Passengers board from a platform that is 2 meters above the ground. What is the equation that models the height above the ground as a function of time in minutes?

• 135 meters

• 137 meters

• 67.5 meters

• 2 meters

3. A person’s blood pressure can be modeled by the function f(t) = 20 sin(160πt) + 100, where f(t) represents the blood pressure at time t, measured in minutes. What is the period of the function?

• 0.0125 minutes

• 0.025 minutes

• 0.05 minutes

• 0.1 minutes

The voltage V, produced in an alternating current generator can be modeled by V(t) = 220 sin(120πt). Find the amplitude and period.

• Amplitude: 220, Period: 1/60

• Amplitude: 220, Period: 1/120

• Amplitude: 110, Period: 1/60

• Amplitude: 110, Period: 1/120

If a resistance of R = 20 ohms is present, what is the current I? Use Ohm’s Law V = IR.

• I = 0.5 A

• I = 1 A

• I = 2 A

• I = 5 A

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CCSS.6.EE.B.7

Fine the amplitude and period of the current I.

• Amplitude: 5A, Period: 2s

• Amplitude: 10A, Period: 4s

• Amplitude: 15A, Period: 6s

• Amplitude: 20A, Period: 8s

A buoy in the Gulf of Mexico sends a signal beacon to a Coast Guard station. The behavior of the buoy can be modeled by the function h = a sin(bt) + 4.5, where h is measured in feet above sea level. During a recent tropical storm, the height varies from 1 foot to 8 feet with a 4.5 second interval between one 8-foot height to the next. Find the values of the constants a and b.

In Miami, FL., there are 12 hours 45 minutes of sunlight on the summer solstice, but only 10 hours 35 minutes of sunlight on the winter solstice. Write a function that models this data using the format: y = A sin[B(x – C)] + D.

• A = 1.05, B = 0.0172, C = 172, D = 11.65

• A = 2.1, B = 0.0344, C = 172, D = 11.65

• A = 1.05, B = 0.0172, C = 355, D = 11.65

• A = 2.1, B = 0.0344, C = 355, D = 11.65

Use the model from A to predict the number of hours of sunlight on April 1, the 91st day of the year.

• 10 hours

• 12 hours

• 14 hours

• 16 hours

A piston operates by a wheel rotating at a constant rate, ω radians per second. The back-and-forth motion of the piston is an example of simple harmonic motion. In a mechanical piston, like shown at right, a wheel with a 6-cm radius turns with an angular velocity of 6π radians/second. Use d = a cos(ωt). A. What is the frequency of the piston?

• 1 Hz

• 2 Hz

• 3 Hz

• 6 Hz