Precalculus Trig Lab
Modeling Circular Functions
Names:
Date:
Hr:
Express all “B” coefficients in  fractions and all other numbers 3 places behind the decimal. Make
sure to mark the axes in the units they represent and include units in sentence answers.
1. Tarzan Problem: Tarzan is swinging back and forth on his grapevine. As he swings, he goes back
and forth across the riverbank, going alternately over land and water. Jane starts her stopwatch
(that she found in the jungle). Letting t be the number of seconds the stopwatch reads and d(t)
the number of feet Tarzan is from the river bank, assume d(t) varies sinusoidally with t and d(t) is
positive when Tarzan is over the water and negative when he is over the land. Jane finds that when
the stopwatch reads 2 seconds, Tarzan is at one end of his swing 28 feet over land and when the
stopwatch reaches 8 seconds Tarzan is at the other end of his swing 20 feet over the water.
(a) Sketch one period of the graph of this sinusoidal function. Make sure to label the axis (d(t) and t)
with appropriate units and mark off appropriate
points. (5 pts)
(b) What is the amplitude & period
(Include units) (2 pts each)
Dar
n!
Amplitude _______________Period___________
(c) Write the equation of curve expressing Tarzan’s distance d(t) from the riverbank in terms of t.
(d) Where will Tarzan be when the time is 2.8 seconds?
(4 pts)
(answer in sentence with units that makes sense to the story)
(3 pts)
(e) Find the third time Tarzan crosses the riverbank. (Answer in sentence with units.)
(2 pts)
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2. High and Low Tides: The depth of the water at the end of the wharf varies with the tides
throughout the day. Today the high tide occurs at 4:15 a.m. with a depth of 15.2 ft. The low tide
occurs at 10:27 a.m. with a depth of 6.0 ft.
(a) Sketch one period of the graph that models the depth d(t) of the water t hours after midnight.
(Label axes with correct units and variables) (5 pts)
(b) What is the amplitude & period
(Include units) (2 pts each)
Amplitude _________________
(c) Write an equation for your curve.
Period_______________
(4 pts)
__
(d) Find the depth of the water at noon: (don’t forget units)
____(2 pts)
(e) A large boat needs at least 9 ft of water to moor at the end of the pier. During what time
period after noon can it safely moor?
to ______
__
(Specify clock time in a.m. and p.m.) (2 pts)
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3. Ferris Wheel Problem: Picture yourself on a Ferris wheel similar to the picture. When the last seat
is filled, your seat is somewhere on the right side of the wheel. The Ferris wheel starts going
counterclockwise and you find that it takes you 3 seconds to reach the top and the wheel makes a
revolution every 8 seconds.
(a) Sketch one period of the graph of your distance from the ground over time (label axes with the
correct units and variables) (5 pts)
50 ft
10 ft
ground
(b) What is the amplitude & period (Include units)
Amplitude _______
(c) Write an equation for your curve.
(2 pts. each)
_ Period________
_______
(2 pts each)
(4 pts)
(d) Predict your height above ground when t = 6 seconds:
(e) At what time are you 18 feet above ground for the third time after 3 seconds?
(2 pts)
(2 pts)
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4. Bouncing Spring: A piece of cardboard is attached to the end of the long Slinky spring above the CBR
(motion detector). Run the Program CBL/CBR APP on the TI-84 calculator, (3: Ranger> Sample > feet >
START NOW) Before you hit enter to start collecting the data, start the spring bouncing. Once the bounce
is consistent ENTER to collect the data. Once the graph is recorded, press ENTER: > SHOW PLOT and trace
to determine your maximum and minimum heights and period.
(a) Fill in the real world measurements with correct units on the figure.
(b) Sketch a graph of the distance of the cardboard from the motion
detector compared to the time. (Label axes) (5 pts)
(c) What is the amplitude & period (Include units)
Amplitude _______
(2 pts. each)
_ Period________
_______
(d) Write an equation for your curve. Put the equation in your calculator and check it with the plotted pts.
(4 pts)
(e) Predict the height of the cardboard from the top of the motion detector after 5 seconds
______________ (2 pts)
(f) When is the third time that the cardboard is at the midline of the curve?
(2 pts)
(g) Change the equation to a sine curve with a positive “A” coefficient and a “B” coefficient that is
rounded 3 decimal places. Remember- replace x with (x-π/2) : y = Asin (B(x - π/2)+C)+D (1 pts)
(h) Find the calculator sinusoidal regression equation: (remember: STAT Calc, C: SinReg, L1, L2, y1)
(1 pt)
(i) Discuss the inconsistencies (changes in A, B, C, or D) that might occur and why it may not be a
normal sinusoidal graph. (1 pt)
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5. Pebble-in-the-Tire Problem: Consider the scale model of a truck. Assume that there is a pebble
lodged in the treads of one of the tires. As the truck rolls along the highway, the pebble’s
distance from the road changes.
(a) Fill in the real world measurements for the toy tire (scale 1 in. to 10 in.) with correct units on the
tire below. (Round all measurements to the nearest ¼ inch on the ruler)
(b) Sketch one period of the graph of the distance of the pebble from
the road compared to the distance traveled in inches starting with the
pebble on the desk. (Label axes) (5 pts)
(c) What is the amplitude & period (Include units)
(2 pts. each)
Amplitude _______________Period_______________
(c) Write an equation for your curve.
(4 pts)
(d) Predict the distance from the road when the tire has traveled 3 feet.
(e) What are the first two distances when the pebble is 1 foot from the road?
(f) If the truck rolls faster will the period or amplitude change? Explain.
(g) What would the independent and dependent variable be for the period to change when the truck
rolls faster?
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6. Pendulum: Using the pendulum and ruler, measure the height of the pendulum (to the nearest inch)
above the ruler on the stand’s platform when it is at rest. Swing the pendulum up about 8 inches
above the flat ruler. Using the stopwatch, record the time it takes for four complete swings of
the pendulum. (back and forth is a complete swing)
(a) Fill in the real world measurements with correct units on the figure to the right.
(b) Sketch one period of the graph of the distance of the weight from the ruler
compared to the time starting with the weight at maximum height. (Label axes) (5 pts.)
(c) What is the amplitude & period? (Include units) (2 pts. each)
Amplitude _______
_ Period________
_______
(2 pts each)
(d) Write an equation for your curve.
(4 pts.)
(e) Predict the height of the weight from the flat ruler after 5 seconds.
(2 pts.)
(f) When is the third time when the weight is 7 inches from the flat ruler?
(2 pts.)
(g) Discuss the inconsistencies (changes in A, B, C, or D) that might occur and why it may not be a
normal sinusoidal graph.
(2 pts.)