1
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Sæt udtrykkene i rækkefølge efter værdi.

2
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Du kan sætte et vilkårligt antal kort
i en kategori

3
00:00:05,640 --> 00:00:07,717
eller have en tom kategori.

4
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Vi har her et diagram

5
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så har vi disse kort med udtryk.

6
00:00:12,310 --> 00:00:15,416
og vi skal sorterer dem i disse bunker.

7
00:00:15,416 --> 00:00:16,790
vi skal altså prøve at sige

8
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hvad er længden af linjestykke AC over længden af

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linjestykke BC?

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Hvilke af disse udtryk er lig med det?

11
00:00:23,130 --> 00:00:27,109
Så skal vi trække det over i det rette felt.

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For at finde ud af dem,

13
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så har jeg allerede genlavet opgave

14
00:00:32,750 --> 00:00:35,050
på min lille scratchpad eller tavle

15
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eller hvad du vil kalde det.

16
00:00:36,220 --> 00:00:37,960
Her er det samme diagram.

17
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bare en smule større.

18
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Her er udtrykene som vi skal trække derover.

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Her er de spande vi skal bruge

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til at finde ud af hvilke af disse udtryk der er lig

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med hvilke af disse udtryk.

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Lad os se på den første.

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Længden af linjestykke AC over
længden af linjestykke BC.

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Lad os se på hvad AC er.

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Længden af linjestykke AC.

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AC er lige her.

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Denne længde her i lilla over

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længen af linjestykke BC, altså over
denne længde her.

29
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Det er forholdet mellem

30
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to sider i en retvinklet trekant.

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Dette er tydeligvis en retvinklet trekant
trekant ABC:

32
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Jeg farver den lige, så du kan se,

33
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hvilken trekant jeg mener.

34
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Trekant ABC er hele denne trekant,

35
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som vi skal se på.

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Du kan nok se at det er rimeligt

37
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at forholdet mellem to af siderne i en retvinklet trekant

38
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er lig sinus til en af dets vinkler.

39
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Og de giver os en af vinklerne her.

40
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De giver os denne vinkel her.

41
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Du siger, men de mærkede blot vinklen.

42
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ja men se, en bue her og en bue her.

43
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Så de steder vi ser en bue,
så er det 30 grader.

44
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Dette er også 30 grader.

45
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Du har to buer her, så det er 41 grader.

46
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To buer her, så den er kongruent med den.

47
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Denne her er 41 grader.

48
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Denne har tre buer.

49
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De fortæller os ikke, hvor mange grader det er,

50
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men den vinkel med tre buer

51
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er kongruent med denne vinkel med tre buer

52
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lige her over.

53
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Så okay, denne gule trekant,
trekant ABCm

54
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vi ved, at vinkelmålet af denne
vinkel er 30 grader.

55
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Vi er givet disse to sider.

56
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Hvilken sammenhæng er der mellem disse sider
og denne 30-graders vinkel?

57
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Side AC er hosliggende til den.

58
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Det er bogstaveligt talt en af de vinkler der udgør vinkel

59
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som ikke er hypotenusen. Lad mig skrive det ned.

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Den er hosliggende

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Hvad er BC?

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BC er hypotensen i denne retvinklet trekant.

63
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Deter siden overfor de 90 grader.

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Dette er hypotensuen.

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Hvilken trig funktion for de 30 grader

66
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er lig den hosliggende side over hypostenuen?

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Lad mig skrive "mod hos modhos", for lige at minde os selv om det.

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"mod hos modhos"

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sinus til en vinkel er modstående over hypotenusen.

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Cosinus til en vinkle er hosliggende over hypotensen.

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cos30

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er lig længden af den hosliggende side

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det er AC over længden af hypotensuen

74
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som er lig BC.

75
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Dette er det samme som

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cos30.

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Lad os trække den derover.

78
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Dette er lig cos30.

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Lad os se på den næste.

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Cosinus til vinkel DEC.

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Hvor er DEC?

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DEC, D E C, det er den vinkel derover.

83
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Jeg laver fire buerher så vi ikke bliver forvirret.

84
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Dette er vinkel DEC.

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Hvad er cosinus til DEC?

86
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Igen, cosinus er hosliggende over hypotensen.

87
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Cosinus til vinkel DEC, den hosliggende side er denne her.

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