Precalculus D – 7.8Sinusoidal Models WorksheetName Answer Key
Date: Block
Use variables that represent what they are, such as time. On all word problems include UNITS on your final equation!
Find an equation that matches the set of data using the given trig function.
1.Use sine2.Use cosine
3.In 1851, after two earlier pendulum experiments, Foucault suspended a ball weighing 61 pounds on a steel wire from the dome of the Pantheon in Paris. If one were to replicate the experiment with technology today, placing a motion detector on the wall near the pendulum and assuming a pivot angle of 50°, one would find a stat plot of the data similar to:
a.Use cosine to find a mathematical model for the pendulum and explain the meaning of each value.
b.The formula can be used to determine the time of the period T of a pendulum given the length L of the pendulum and the force of gravity g. Use the standard value of gravity on Earth of 9.81 m/sec2 to determine the length of Foucault’s pendulum.
4.According to as of 08 Feb 2011 the average monthly temperature in °F for Orlando, FL each month is the following:
Jan59.7
Feb61.2
Mar66.7
Apr71.2
May76.9
Jun81.1
Jul82.3
Aug82.5
Sep81.0
Oct75.2
Nov68.0
Dec62.1
a.Use sine to find a mathematical model for the average monthly temperature of Orlando and explain the meaning of each value.
Using SinReg on the calculator the following equation is developed:
Rewriting it in the normal form we use leaves us with
b.How does this model differ from the average monthly temperature model for Lincoln, NE? Why do you think those differences exist?
5.According to of 05 Feb 2010 the average hours of sunlight per day for Lincoln, NE is the following:
Jan9.64(Day 17)
Feb10.67(Day 46)
Mar11.97(Day 75)
Apr13.32(Day 105)
May14.47(Day 136)
Jun15.05(Day 162)
Jul14.76(Day 199)
Aug13.75(Day 228)
Sep12.45(Day 258)
Oct11.10(Day 289)
Nov9.92(Day 319)
Dec9.31(Day 345)
a.Use sine to find a mathematical model for the average hours of sunlight (hours) on a given day for Lincoln and explain the meaning of each value.
Using SinReg on the calculator the following equation is developed:
Rewriting it in the normal form we use leaves us with:
b.What amount of sunlight does the model predict for day 123? 576?
Using rounded function:
Using VALUE command on calculator’s graph:
6.A motion detector is facing the floor as it revolves around a circle. The following graph of height (m) vs time (sec) was obtained following the collection of data.
a.Use sine to find a mathematical model for the circle and explain the meaning of each value.
b. What is the angular velocity (rpm) and linear velocity (mph) of the wheel?
7.Engineers at the Silver Hawk Summer Festival are attempting to model the motion of the Ferris wheel. The Ferris wheel has a radius of 24 ft and the rider is 3 ft above the ground at the lowest point. When operating at full speed, the rider makes one counter-clockwise revolution every 90 seconds.
a.Use sine to write a function to model the height of the rider starting with t = 0 sec when the rider reaches point A at the top of the Ferris wheel. Explain the meaning of each value of the function.
b.Use the TRACE feature of your graphing calculator to estimate the time it would take the rider to be going up and 20 feet above the ground.