Graphing Sine and Cosine Answers
b = ,
c =
The vertical shift is .
An equation for this graph is y = .
The minimum height reached by the barnacleis m.
PENDING
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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a = ,
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d = ⇒ 1
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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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.
Find the following (take ground level to be 0):Gum’s minimum height: ft Gum’s maximum height: ft
a = [___], b = [___], c = [___], d = [___], e = [___]
1, 3, -2, -12, -8
Graph the following points on the graphing calculator: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.
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.
e =
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