Daily Desmos 88b - by Justin Lanier (talljerome solution)
Expression 10: "y" equals StartFraction, .7 5 Over pi , EndFraction arc cosine left parenthesis, negative cos left parenthesis, StartFraction, 2 pi Over 3 , EndFraction "x" , right parenthesis , right parenthesis plus .7 5 plus StartAbsoluteValue, StartFraction, .7 5 Over pi , EndFraction arccos left parenthesis, negative cos left parenthesis, StartFraction, 2 pi Over 3 , EndFraction "x" , right parenthesis , right parenthesis minus .2 5 , EndAbsoluteValuey=.75πarccos−cos2π3x+.75+.75πarccos−cos2π3x−.25
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Expression 11: "y" equals 1 third cosine StartFraction, 2 pi Over 3 , EndFraction "x" plus 1 third StartAbsoluteValue, cos StartFraction, 2 pi Over 3 , EndFraction "x" plus 1 half , EndAbsoluteValue plus 7 sixthsy=13cos2π3x+13cos2π3x+12+76
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Expression 12: "y" equals 8 cosine StartFraction, 2 pi Over 3 , EndFraction "x" plus 8 StartAbsoluteValue, cos StartFraction, 2 pi Over 3 , EndFraction "x" minus StartFraction, 15 Over 16 , EndFraction , EndAbsoluteValue minus 6.5y=8cos2π3x+8cos2π3x−1516−6.5
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Expression 13: "y" equals 2 thirds StartAbsoluteValue, cos left parenthesis, StartFraction, pi Over 3 , EndFraction "x" , right parenthesis plus cos left parenthesis, pi "x" , right parenthesis , EndAbsoluteValue plus 2 thirdsy=23cosπ3x+cosπx+23
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Expression 14: "y" equals StartFraction, 6 "n" plus left parenthesis, negative 1 , right parenthesis Superscript, "m" , Baseline Over 3 "n" , EndFraction StartAbsoluteValue, cos left parenthesis, StartFraction, pi Over 3 , EndFraction "x" , right parenthesis minus StartFraction, left parenthesis, negative 1 , right parenthesis Superscript, "m" , Baseline Over 6 "n" plus left parenthesis, negative 1 , right parenthesis Superscript, "m" , Baseline , EndFraction cos left parenthesis, StartFraction, left parenthesis, 6 "n" plus left parenthesis, negative 1 , right parenthesis Superscript, "m" , Baseline , right parenthesis pi Over 3 , EndFraction "x" , right parenthesis , EndAbsoluteValuey=6n+−1m3ncosπ3x−−1m6n+−1mcos6n+−1mπ3x
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For above graph, value of m determines whether the provided points are minima or maxima. Value of n determines number of local extrema over each period.