Expression 13: "f" Subscript, 2 , Baseline left parenthesis, "X" , right parenthesis equals arc tangent left parenthesis, "X" . "y" , "X" . "x" , right parenthesisf2X=arctanX.y,X.x
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Expression 14: "f" Subscript, 3 , Baseline left parenthesis, "X" , right parenthesis equals StartFraction, left brace, "f" Subscript, 2 , Baseline left parenthesis, "X" , right parenthesis less than 0 : "f" Subscript, 2 , Baseline left parenthesis, "X" , right parenthesis plus 2 pi , "f" Subscript, 2 , Baseline left parenthesis, "X" , right parenthesis , right brace Over 2 pi , EndFraction 360f3X=f2X<0:f2X+2π,f2X2π360
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Expression 15: "f" Subscript, 4 , Baseline left parenthesis, "X" , right parenthesis equals StartFraction, "f" Subscript, 2 , Baseline left parenthesis, "X" , right parenthesis plus pi Over 2 pi , EndFraction 360f4X=f2X+π2π360
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Expression 16: "f" Subscript, 5 , Baseline left parenthesis, "X" , right parenthesis equals StartFraction, left brace, "f" Subscript, 2 , Baseline left parenthesis, "X" , right parenthesis less than 0 : mod left parenthesis, "f" Subscript, 2 , Baseline left parenthesis, "X" , right parenthesis plus StartNestedFraction, 5 pi NestedOver 2 , EndNestedFraction , 2 pi , right parenthesis , "f" Subscript, 2 , Baseline left parenthesis, "X" , right parenthesis plus StartNestedFraction, pi NestedOver 2 , EndNestedFraction , right brace Over 2 pi , EndFraction 360f5X=f2X<0:modf2X+5π2,2π,f2X+π22π360
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Expression 17: "f" Subscript, 6 , Baseline left parenthesis, "X" , right parenthesis equals StartFraction, left brace, "f" Subscript, 2 , Baseline left parenthesis, "X" , right parenthesis less than 0 : "f" Subscript, 2 , Baseline left parenthesis, "X" , right parenthesis plus StartNestedFraction, 3 pi NestedOver 2 , EndNestedFraction , mod left parenthesis, "f" Subscript, 2 , Baseline left parenthesis, "X" , right parenthesis plus StartNestedFraction, 3 pi NestedOver 2 , EndNestedFraction , 2 pi , right parenthesis , right brace Over 2 pi , EndFraction 360f6X=f2X<0:f2X+3π2,modf2X+3π2,2π2π360
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Expression 18: "f" Subscript, 7 , Baseline left parenthesis, "X" , right parenthesis equals left brace, "f" Subscript, 8 , Baseline left parenthesis, "X" , right parenthesis equals 0 : "f" Subscript, 3 , Baseline left parenthesis, "X" , right parenthesis , "f" Subscript, 8 , Baseline left parenthesis, "X" , right parenthesis equals 1 : "f" Subscript, 6 , Baseline left parenthesis, "X" , right parenthesis , "f" Subscript, 8 , Baseline left parenthesis, "X" , right parenthesis equals 2 : "f" Subscript, 3 , Baseline left parenthesis, "X" , right parenthesis , "f" Subscript, 8 , Baseline left parenthesis, "X" , right parenthesis equals 3 : "f" Subscript, 6 , Baseline left parenthesis, "X" , right parenthesis , right bracef7X=f8X=0:f3X,f8X=1:f6X,f8X=2:f3X,f8X=3:f6X
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Expression 19: "f" Subscript, 8 , Baseline left parenthesis, "X" , right parenthesis equals 2 times absolute value left parenthesis, floor left parenthesis, StartFraction, mod left parenthesis, "f" Subscript, 0 , Baseline left parenthesis, "X" , right parenthesis , 4 , right parenthesis Over 2 , EndFraction , right parenthesis minus abs left parenthesis, floor left parenthesis, StartFraction, mod left parenthesis, "L" , 4 , right parenthesis Over 2 , EndFraction , right parenthesis mod left parenthesis, floor left parenthesis, StartFraction, "f" Subscript, 0 , Baseline left parenthesis, "X" , right parenthesis Over "L" , EndFraction , right parenthesis , 2 , right parenthesis minus floor left parenthesis, StartFraction, mod left parenthesis, floor left parenthesis, StartNestedFraction, "f" Subscript, 0 , Baseline left parenthesis, "X" , right parenthesis NestedOver "L" , EndNestedFraction , right parenthesis , 4 , right parenthesis Over 2 , EndFraction , right parenthesis , right parenthesis , right parenthesis plus absolute value left parenthesis, mod left parenthesis, "f" Subscript, 0 , Baseline left parenthesis, "X" , right parenthesis , 2 , right parenthesis minus mod left parenthesis, floor left parenthesis, StartFraction, "f" Subscript, 0 , Baseline left parenthesis, "X" , right parenthesis Over "L" , EndFraction , right parenthesis , 2 , right parenthesis , right parenthesisf8X=2·absfloormodf0X,42−absfloormodL,42modfloorf0XL,2−floormodfloorf0XL,42+absmodf0X,2−modfloorf0XL,2
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Expression 20: "g" left parenthesis, "X" , right parenthesis equals left brace, StartRoot, "X" . "x" squared plus "X" . "y" squared , EndRoot less than or equal to 1 : sin left parenthesis, StartFraction, pi Over 2 , EndFraction StartRoot, "X" . "x" squared plus "X" . "y" squared , EndRoot , right parenthesis left parenthesis, cos left parenthesis, arctan left parenthesis, "X" . "y" , "X" . "x" , right parenthesis , right parenthesis , sin left parenthesis, arctan left parenthesis, "X" . "y" , "X" . "x" , right parenthesis , right parenthesis , right parenthesis , "X" , right bracegX=X.x2+X.y2≤1:sinπ2X.x2+X.y2cosarctanX.y,X.x,sinarctanX.y,X.x,X
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Expression 21: "g" left parenthesis, 7 sixths StartFraction, 2 Over "L" , EndFraction left parenthesis, "s" left parenthesis, "t" , right parenthesis minus left parenthesis, StartFraction, "L" minus 1 Over 2 , EndFraction , StartFraction, "L" minus 1 Over 2 , EndFraction , right parenthesis , right parenthesis , right parenthesisg762Lst−L−12,L−12
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Expression 22: "g" left parenthesis, 7 sixths StartFraction, 2 Over "L" , EndFraction left parenthesis, "c" left parenthesis, "t" , right parenthesis minus left parenthesis, StartFraction, "L" minus 1 Over 2 , EndFraction , StartFraction, "L" minus 1 Over 2 , EndFraction , right parenthesis , right parenthesis , right parenthesisg762Lct−L−12,L−12
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Expression 23: StartFraction, left parenthesis, sin left parenthesis, 10 pi "t" , right parenthesis plus left parenthesis, "a" plus 6 fifths , right parenthesis , right parenthesis Over left parenthesis, "a" plus 11 fifths , right parenthesis , EndFraction StartFraction, 16 "L" Over 37 , EndFraction left parenthesis, cos left parenthesis, 2 pi "t" , right parenthesis , sin left parenthesis, 2 pi "t" , right parenthesis , right parenthesis plus left parenthesis, StartFraction, "L" Over 2 , EndFraction minus 1 half , StartFraction, "L" Over 2 , EndFraction minus 1 half , right parenthesissin10πt+a+65a+11516L37cos2πt,sin2πt+L2−12,L2−12
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Expression 24: left parenthesis, StartFraction, "a" Over length left parenthesis, "a" , right parenthesis , EndFraction , right parenthesis Superscript, 1 half , Baseline StartFraction, 16 "L" Over 37 , EndFraction left parenthesis, cos left parenthesis, 2 pi "t" , right parenthesis , sin left parenthesis, 2 pi "t" , right parenthesis , right parenthesis plus left parenthesis, StartFraction, "L" Over 2 , EndFraction minus 1 half , StartFraction, "L" Over 2 , EndFraction minus 1 half , right parenthesisalengtha1216L37cos2πt,sin2πt+L2−12,L2−12
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Expression 25: left parenthesis, StartFraction, "a" Over length left parenthesis, "a" , right parenthesis , EndFraction , right parenthesis StartFraction, 16 "L" Over 37 , EndFraction left parenthesis, cos left parenthesis, 2 pi "t" , right parenthesis , sin left parenthesis, 2 pi "t" , right parenthesis , right parenthesis plus left parenthesis, StartFraction, "L" Over 2 , EndFraction minus 1 half , StartFraction, "L" Over 2 , EndFraction minus 1 half , right parenthesisalengtha16L37cos2πt,sin2πt+L2−12,L2−12
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Expression 26: "a" equals left bracket, 0...2 0 , right bracketa=0...20