Graphing Sine And Cosine

25 July 2022
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16 test answers

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question
The maximum height reached by the barnacle is ______ m.
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1
question
The minimum height reached by the barnacle is ______ m.
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-1
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How far does the barnacle travel in one revolution of the water wheel?
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D. 2pi
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The boat is traveling at a rate of 1 meter per second. How long does it take the barnacle to get back to its starting point?
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D. 2π seconds
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Complete the table. *has a table about time, distance, and height. Time is measured in obscure increments of π*
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Distances: a = 1/2π b = 1π c = 3/2π Heights: d = 1 e = 0 f = -1
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The data from the previous table is plotted to the right. The distance the boat traveled is on the x-axis, and the vertical position of the barnacle is on the y-axis. The graph follows the ______ pattern.
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zero-max-zero-min-zero
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This is the pattern for a ______ function.
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sine
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The amplitude is The vertical shift is An equation for this graph is y =
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1 0 sin x
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Graph y = sin(x) on the graphing calculator. Use the graph to determine the height of the barnacle with respect to water level as the boat has traveled the given distance. When the boat has traveled 7 meters, the height of the barnacle is approximately:
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C. 0.657
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When the boat has traveled 10 meters, the height of the barnacle is approximately:
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B. -0.544
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Explain how to determine the following from the graph: Number of times the barnacle went beneath the water level if the boat traveled a distance of 20 m Number of meters of the 20 m trip that the barnacle was underwater Check each of the following that you included in your explanation.
answer
When the graph is below the x-axis, the barnacle is underwater. The graph dips below the x-axis three times between x = 0 and x = 20, so the barnacle goes underwater three times. Every time the barnacle goes underwater, the boat travels meters (one half the circumference of the wheel) before the barnacle comes back up, so the barnacle covers 3 meters underwater between x = 0 and x = 20.
question
A rider is riding a bicycle on a 6-foot wall at a rate of 1 foot per second. The wheels have a radius of 1 foot, and a piece of gum becomes stuck to the rear wheel as shown, continuing to travel with the bicycle. Find the following (take ground level to be 0):
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Gum's minimum height: 6 ft Gum's maximum height: 8 ft
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How far does the gum travel in one revolution of the bicycle wheel?
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2pi ft
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Complete the table. *table with Distance and Height. Distance is measured with π feet. π feet.*
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a = 6 b = 7 c = 8 d = 7 e = 6
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Graph the following points on the graphing calculator: *(0,6), (π/2, 7), (π, 8), and I don't want to type the rest* Explain how to use the graph to write an equation to model the gum's height. Be sure to identify the pattern of the points in your explanation, and identify the values of a and k.
answer
The pattern is min-zero-max-zero-min, which is the pattern for a cosine function of the form y = acos(x) + k, but is reflected over the x-axis (so a < 0). The amplitude is |a|, so a = -1 and |a| = 1. The midline is exactly between the max and the min, y = (6 + 8)/2 = 7, so k = 7. The equation is y = -cos(x) + 7.
question
Graph the function y = -cos(x) + 7 and explain how to find the number of times the gum returns to the wall as it travels a distance of 60 feet.
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The gum returns to the wall each time the graph shows a minimum value of 6 (the height of the wall). Count the number of minimums that occur between x = 0 ft and x = 60 (but omit the first time when x = 0). The gum returns to the wall 9 times while traveling a distance of 60 feet.