Expression 15: "x" Subscript, "a" "r" "r" , Baseline left parenthesis, "t" , "x" Subscript, "s" , Baseline , "y" Subscript, "s" , Baseline , right parenthesis equals left brace, 0 less than "t" less than "l" : "x" Subscript, "s" , Baseline "t" , "l" less than "t" less than StartFraction, "l" plus 1 Over 2 , EndFraction : "l" "x" Subscript, "s" , Baseline plus cos left parenthesis, StartFraction, 5 pi Over 6 , EndFraction , right parenthesis "x" Subscript, "s" , Baseline left parenthesis, "t" minus "l" , right parenthesis minus sin left parenthesis, StartFraction, 5 pi Over 6 , EndFraction , right parenthesis "y" Subscript, "s" , Baseline left parenthesis, "t" minus "l" , right parenthesis , StartFraction, "l" plus 1 Over 2 , EndFraction less than "t" less than 1 : "l" "x" Subscript, "s" , Baseline plus sin left parenthesis, StartFraction, 5 pi Over 6 , EndFraction , right parenthesis "y" Subscript, "s" , Baseline left parenthesis, "t" minus StartFraction, "l" plus 1 Over 2 , EndFraction , right parenthesis plus cos left parenthesis, StartFraction, 5 pi Over 6 , EndFraction , right parenthesis "x" Subscript, "s" , Baseline left parenthesis, "t" minus StartFraction, "l" plus 1 Over 2 , EndFraction , right parenthesis , right bracexarrt,xs,ys=0<t<l:xst,l<t<l+12:lxs+cos5π6xst−l−sin5π6yst−l,l+12<t<1:lxs+sin5π6yst−l+12+cos5π6xst−l+12
15
Expression 16: "y" Subscript, "a" "r" "r" , Baseline left parenthesis, "t" , "x" Subscript, "s" , Baseline , "y" Subscript, "s" , Baseline , right parenthesis equals left brace, 0 less than "t" less than "l" : "y" Subscript, "s" , Baseline "t" , "l" less than "t" less than StartFraction, "l" plus 1 Over 2 , EndFraction : "l" "y" Subscript, "s" , Baseline plus cos left parenthesis, StartFraction, 5 pi Over 6 , EndFraction , right parenthesis "y" Subscript, "s" , Baseline left parenthesis, "t" minus "l" , right parenthesis plus sin left parenthesis, StartFraction, 5 pi Over 6 , EndFraction , right parenthesis "x" Subscript, "s" , Baseline left parenthesis, "t" minus "l" , right parenthesis , StartFraction, "l" plus 1 Over 2 , EndFraction less than "t" less than 1 : "l" "y" Subscript, "s" , Baseline minus sin left parenthesis, StartFraction, 5 pi Over 6 , EndFraction , right parenthesis "x" Subscript, "s" , Baseline left parenthesis, "t" minus StartFraction, "l" plus 1 Over 2 , EndFraction , right parenthesis plus cos left parenthesis, StartFraction, 5 pi Over 6 , EndFraction , right parenthesis "y" Subscript, "s" , Baseline left parenthesis, "t" minus StartFraction, "l" plus 1 Over 2 , EndFraction , right parenthesis , right braceyarrt,xs,ys=0<t<l:yst,l<t<l+12:lys+cos5π6yst−l+sin5π6xst−l,l+12<t<1:lys−sin5π6xst−l+12+cos5π6yst−l+12
16
Expression 17: left parenthesis, "x" Subscript, "a" "r" "r" , Baseline left parenthesis, "t" , "a" Subscript, "l" , Baseline "x" Subscript, "x" , Baseline , "a" Subscript, "l" , Baseline "x" Subscript, "y" , Baseline , right parenthesis , "y" Subscript, "a" "r" "r" , Baseline left parenthesis, "t" , "a" Subscript, "l" , Baseline "x" Subscript, "x" , Baseline , "a" Subscript, "l" , Baseline "x" Subscript, "y" , Baseline , right parenthesis , right parenthesisxarrt,alxx,alxy,yarrt,alxx,alxy
Minimum du domaine t: 00
less than or equal to "t" less than or equal to≤t≤
Maximum du domaine t: 11
17
Expression 18: left parenthesis, "x" Subscript, "a" "r" "r" , Baseline left parenthesis, "t" , "a" Subscript, "l" , Baseline "y" Subscript, "x" , Baseline , "a" Subscript, "l" , Baseline "y" Subscript, "y" , Baseline , right parenthesis , "y" Subscript, "a" "r" "r" , Baseline left parenthesis, "t" , "a" Subscript, "l" , Baseline "y" Subscript, "x" , Baseline , "a" Subscript, "l" , Baseline "y" Subscript, "y" , Baseline , right parenthesis , right parenthesisxarrt,alyx,alyy,yarrt,alyx,alyy
Minimum du domaine t: 00
less than or equal to "t" less than or equal to≤t≤
Maximum du domaine t: 11
18
Expression 19: left parenthesis, "x" Subscript, "a" "r" "r" , Baseline left parenthesis, "t" , "a" Subscript, "l" , Baseline "z" Subscript, "x" , Baseline , "a" Subscript, "l" , Baseline "z" Subscript, "y" , Baseline , right parenthesis , "y" Subscript, "a" "r" "r" , Baseline left parenthesis, "t" , "a" Subscript, "l" , Baseline "z" Subscript, "x" , Baseline , "a" Subscript, "l" , Baseline "z" Subscript, "y" , Baseline , right parenthesis , right parenthesisxarrt,alzx,alzy,yarrt,alzx,alzy
Minimum du domaine t: 00
less than or equal to "t" less than or equal to≤t≤
Maximum du domaine t: 11
19
And, finally, we draw the graph in blue and green. Can you figure out what g(t) and h(t) do?
20
Expression 21: "g" left parenthesis, "x" , right parenthesis equals 2 "s" left parenthesis, StartFraction, floor left parenthesis, "x" times left parenthesis, "n" plus 1 , right parenthesis , right parenthesis Over "n" , EndFraction minus .5 , right parenthesisgx=2sfloorx·n+1n−.5
21
Expression 22: "h" left parenthesis, "x" , right parenthesis equals 2 "s" left parenthesis, mod left parenthesis, "x" times left parenthesis, "n" plus 1 , right parenthesis , 1 , right parenthesis minus .5 , right parenthesishx=2smodx·n+1,1−.5
22
Expression 23: left parenthesis, "x" Subscript, "x" , Baseline "g" left parenthesis, "t" , right parenthesis plus "y" Subscript, "x" , Baseline "h" left parenthesis, "t" , right parenthesis plus "z" Subscript, "x" , Baseline "f" left parenthesis, "g" left parenthesis, "t" , right parenthesis , "h" left parenthesis, "t" , right parenthesis , right parenthesis , "x" Subscript, "y" , Baseline "g" left parenthesis, "t" , right parenthesis plus "y" Subscript, "y" , Baseline "h" left parenthesis, "t" , right parenthesis plus "z" Subscript, "y" , Baseline "f" left parenthesis, "g" left parenthesis, "t" , right parenthesis , "h" left parenthesis, "t" , right parenthesis , right parenthesis , right parenthesisxxgt+yxht+zxfgt,ht,xygt+yyht+zyfgt,ht
Minimum du domaine t: 00
less than or equal to "t" less than or equal to≤t≤
Maximum du domaine t: 11
23
Expression 24: left parenthesis, "x" Subscript, "x" , Baseline "h" left parenthesis, "t" , right parenthesis plus "y" Subscript, "x" , Baseline "g" left parenthesis, "t" , right parenthesis plus "z" Subscript, "x" , Baseline "f" left parenthesis, "h" left parenthesis, "t" , right parenthesis , "g" left parenthesis, "t" , right parenthesis , right parenthesis , "x" Subscript, "y" , Baseline "h" left parenthesis, "t" , right parenthesis plus "y" Subscript, "y" , Baseline "g" left parenthesis, "t" , right parenthesis plus "z" Subscript, "y" , Baseline "f" left parenthesis, "h" left parenthesis, "t" , right parenthesis , "g" left parenthesis, "t" , right parenthesis , right parenthesis , right parenthesisxxht+yxgt+zxfht,gt,xyht+yygt+zyfht,gt
Minimum du domaine t: 00
less than or equal to "t" less than or equal to≤t≤
Maximum du domaine t: 11
24
Étiquette masqué left parenthesis, "a" , "b" , right parenthesisa,b
Étiquette
25
Expression 26: "z" "x"zx
26
Expression 27: "z" equals 0.7z=0.7
negative 10−10
1010
27
Expression 28:
28
Expression 29: "d" equals negative 0.5d=−0.5
negative 5−5
55
29
Expression 30:
30
31
propulsé par
propulsé par
"x"x
"y"y
"a" squareda2
"a" Superscript, "b" , Baselineab
77
88
99
over÷
fonctions
((
))
less than<
greater than>
44
55
66
times×
| "a" ||a|
,,
less than or equal to≤
greater than or equal to≥
11
22
33
negative−
A B C
StartRoot, , EndRoot
piπ
00
..
equals=
positive+
ou
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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
exemple
Paramétrique : Cycloïde
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Transformations : Translation de fonctions
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Transformations : Compression et étirement de fonctions