Hidden Label: left parenthesis, "a" , "M" left parenthesis, "a" , right parenthesis , right parenthesis equals left parenthesis, 273 , negative 3.1 6 0 3 3 0 0 1 7 8 2 , right parenthesisa,Ma
Label
equals=
left parenthesis, 273 , negative 3.1 6 0 3 3 0 0 2 , right parenthesis273,−3.16033002
18
N(t) is periodic, because it restarts at the beginning of every year. What can you say about the derivative of a periodic function? Explain your answer. Answer:
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When you have answered all of the questions above, save this graph and share it with me.
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The next cell contains the formula for N(t). Its exact form is not important for us. Below it are other formulas used in the definition of N(t). You can ignore everything below this cell for purposes of this project.
21
Expression 22: "N" left parenthesis, "t" , right parenthesis equals "H" times StartFraction, arccos left parenthesis, "T" left parenthesis, tan left parenthesis, "L" , right parenthesis tan left parenthesis, "A" times cos left parenthesis, StartNestedFraction, 360 NestedOver "D" , EndNestedFraction left parenthesis, "t" plus "S" , right parenthesis , right parenthesis , right parenthesis , right parenthesis , right parenthesis Over 180 , EndFractionNt=H·arccosTtanLtanA·cos360Dt+S180
22
H is the maximum number of hours in a day.
23
Expression 24: "H" equals 24H=24
negative 10−10
2424
24
D is the total number of days in a year. Default is 365.
25
Expression 26: "D" equals 365D=365
negative 10−10
400400
26
A is the inclination of Earth's axis with respect to the plane of Earth's orbit. Default is 23.44 degrees.
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Expression 28: "A" equals 23.4 4A=23.44
negative 85−85
8585
28
S is the offset of the start of the year: the number of days after the winter solstice that the year begins. Default is 11 days.
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Expression 30: "S" equals 11S=11
negative 10−10
365365
30
T is a "truncation" function: its outputs lie between %u20131 and 1.
31
Expression 32: "T" left parenthesis, "x" , right parenthesis equals left brace, "x" greater than 1 : 1 , "x" less than negative 1 : negative 1 , negative 1 less than or equal to "x" less than or equal to 1 : "x" , right braceTx=x>1:1,x<−1:−1,−1≤x≤1:x
32
Expression 33: "y" equals "H" equals 24 Has graph. To audio trace, press ALT+T.y=H
