Expression 3: "f" left parenthesis, "x" , right parenthesis equals left brace, "t" less than or equal to "x" less than or equal to "t" plus StartFraction, pi Over 2 , EndFraction : StartFraction, sin left parenthesis, "x" , right parenthesis Over cos left parenthesis, "x" minus "t" , right parenthesis plus sin left parenthesis, "x" minus "t" , right parenthesis , EndFraction , "t" plus StartFraction, pi Over 2 , EndFraction less than "x" less than "t" plus pi : StartFraction, negative sin left parenthesis, "x" , right parenthesis Over cos left parenthesis, "x" minus "t" , right parenthesis minus sin left parenthesis, "x" minus "t" , right parenthesis , EndFraction , "t" plus pi less than "x" less than "t" plus StartFraction, 3 pi Over 2 , EndFraction : StartFraction, negative sin left parenthesis, "x" , right parenthesis Over cos left parenthesis, "x" minus "t" , right parenthesis plus sin left parenthesis, "x" minus "t" , right parenthesis , EndFraction , "t" plus StartFraction, 3 pi Over 2 , EndFraction less than "x" less than "t" plus 2 pi : StartFraction, sin left parenthesis, "x" , right parenthesis Over cos left parenthesis, "x" minus "t" , right parenthesis minus sin left parenthesis, "x" minus "t" , right parenthesis , EndFraction , right bracefx=t≤x≤t+π2:sinxcosx−t+sinx−t,t+π2<x<t+π:−sinxcosx−t−sinx−t,t+π<x<t+3π2:−sinxcosx−t+sinx−t,t+3π2<x<t+2π:sinxcosx−t−sinx−t
3
Expression 4: "f" left parenthesis, "x" , right parenthesis equals left brace, "t" minus 2 pi less than or equal to "x" less than or equal to "t" minus 2 pi plus StartFraction, pi Over 2 , EndFraction : StartFraction, sin left parenthesis, "x" , right parenthesis Over cos left parenthesis, "x" minus "t" , right parenthesis plus sin left parenthesis, "x" minus "t" , right parenthesis , EndFraction , "t" minus 2 pi plus StartFraction, pi Over 2 , EndFraction less than "x" less than "t" minus 2 pi plus pi : StartFraction, negative sin left parenthesis, "x" , right parenthesis Over cos left parenthesis, "x" minus "t" , right parenthesis minus sin left parenthesis, "x" minus "t" , right parenthesis , EndFraction , "t" minus 2 pi plus pi less than "x" less than "t" minus 2 pi plus StartFraction, 3 pi Over 2 , EndFraction : StartFraction, negative sin left parenthesis, "x" , right parenthesis Over cos left parenthesis, "x" minus "t" , right parenthesis plus sin left parenthesis, "x" minus "t" , right parenthesis , EndFraction , "t" minus 2 pi plus StartFraction, 3 pi Over 2 , EndFraction less than "x" less than "t" minus 2 pi plus 2 pi : StartFraction, sin left parenthesis, "x" , right parenthesis Over cos left parenthesis, "x" minus "t" , right parenthesis minus sin left parenthesis, "x" minus "t" , right parenthesis , EndFraction , right bracefx=t−2π≤x≤t−2π+π2:sinxcosx−t+sinx−t,t−2π+π2<x<t−2π+π:−sinxcosx−t−sinx−t,t−2π+π<x<t−2π+3π2:−sinxcosx−t+sinx−t,t−2π+3π2<x<t−2π+2π:sinxcosx−t−sinx−t
4
Expression 5: "f" left parenthesis, "x" , right parenthesis equals left brace, "t" less than or equal to "x" less than or equal to "t" plus StartFraction, pi Over 2 , EndFraction : StartFraction, cos left parenthesis, "x" , right parenthesis Over StartRoot, 2 , EndRoot sin left parenthesis, "x" minus "t" plus StartNestedFraction, pi NestedOver 4 , EndNestedFraction , right parenthesis , EndFraction , "t" plus StartFraction, pi Over 2 , EndFraction less than "x" less than "t" plus pi : StartFraction, cos left parenthesis, "x" , right parenthesis Over StartRoot, 2 , EndRoot sin left parenthesis, "x" minus "t" minus StartNestedFraction, pi NestedOver 4 , EndNestedFraction , right parenthesis , EndFraction , "t" plus pi less than "x" less than "t" plus StartFraction, 3 pi Over 2 , EndFraction : StartFraction, negative cos left parenthesis, "x" , right parenthesis Over StartRoot, 2 , EndRoot sin left parenthesis, "x" minus "t" plus StartNestedFraction, pi NestedOver 4 , EndNestedFraction , right parenthesis , EndFraction , "t" plus StartFraction, 3 pi Over 2 , EndFraction less than "x" less than "t" plus 2 pi : StartFraction, negative cos left parenthesis, "x" , right parenthesis Over StartRoot, 2 , EndRoot sin left parenthesis, "x" minus "t" minus StartNestedFraction, pi NestedOver 4 , EndNestedFraction , right parenthesis , EndFraction , right bracefx=t≤x≤t+π2:cosx2sinx−t+π4,t+π2<x<t+π:cosx2sinx−t−π4,t+π<x<t+3π2:−cosx2sinx−t+π4,t+3π2<x<t+2π:−cosx2sinx−t−π4
5
Expression 6: "f" left parenthesis, "x" , right parenthesis equals left brace, "t" minus 2 pi less than or equal to "x" less than or equal to "t" minus 2 pi plus StartFraction, pi Over 2 , EndFraction : StartFraction, cos left parenthesis, "x" , right parenthesis Over StartRoot, 2 , EndRoot sin left parenthesis, "x" minus "t" plus StartNestedFraction, pi NestedOver 4 , EndNestedFraction , right parenthesis , EndFraction , "t" minus 2 pi plus StartFraction, pi Over 2 , EndFraction less than "x" less than "t" minus pi : StartFraction, cos left parenthesis, "x" , right parenthesis Over StartRoot, 2 , EndRoot sin left parenthesis, "x" minus "t" minus StartNestedFraction, pi NestedOver 4 , EndNestedFraction , right parenthesis , EndFraction , "t" minus pi less than "x" less than "t" minus 2 pi plus StartFraction, 3 pi Over 2 , EndFraction : StartFraction, negative cos left parenthesis, "x" , right parenthesis Over StartRoot, 2 , EndRoot sin left parenthesis, "x" minus "t" plus StartNestedFraction, pi NestedOver 4 , EndNestedFraction , right parenthesis , EndFraction , "t" minus 2 pi plus StartFraction, 3 pi Over 2 , EndFraction less than "x" less than "t" : StartFraction, negative cos left parenthesis, "x" , right parenthesis Over StartRoot, 2 , EndRoot sin left parenthesis, "x" minus "t" minus StartNestedFraction, pi NestedOver 4 , EndNestedFraction , right parenthesis , EndFraction , right bracefx=t−2π≤x≤t−2π+π2:cosx2sinx−t+π4,t−2π+π2<x<t−π:cosx2sinx−t−π4,t−π<x<t−2π+3π2:−cosx2sinx−t+π4,t−2π+3π2<x<t:−cosx2sinx−t−π4
6
7
propulsé par
propulsé par
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"a" Superscript, "b" , Baselineab
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fonctions
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less than<
greater than>
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times×
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greater than or equal to≥
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equals=
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Exemples
Droites : Forme avec la pente et l'ordonnée à l'origine
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Droites : Forme avec la pente passant par un point donné
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Droites : Passant par deux points donnés
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Paraboles : Forme générale
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Paraboles : Forme canonique
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Paraboles : Forme générale + Tangente
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Trigonométrie : Période et Amplitude
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Trigonométrie : Phase
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Trigonométrie : Phase et addition de fonctions
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Trigonométrie : Cercle trigonométrique
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Coniques : Cercle
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Coniques : Parabole et Foyer
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Coniques : Ellipse et Foyers
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Coniques : Hyperbole
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Polaire : Rosace
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Polaire : Spirale logarithmique
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Polaire : Limaçon
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Polaire : Les coniques
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Paramétrique : Introduction
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Paramétrique : Cycloïde
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Transformations : Translation de fonctions
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Transformations : Compression et étirement de fonctions
