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Afsnitte

Vir funksie van die vorm y = sin ( θ + p ) , word die metode om die afsnitte met die y as te bereken gegee.

Die y -afsnit word bereken as volg: stel θ = 0

y = sin ( θ + p ) y afsnit = sin ( 0 + p ) = sin ( p )

Funksies van die vorm y = cos ( θ + p )

In die vergelyking y = cos ( θ + p ) , is p 'n konstante en het verskillende effekte op die grafiek van die funksie. Die algemene vorm van die grafiek van hierdie soort funksies word gegee in [link] for the function f ( θ ) = cos ( θ + 30 ) .

Grafiek van f ( θ ) = cos ( θ + 30 ) (vastelyn) en die grafiek van g ( θ ) = cos ( θ ) (stippellyn).

Funksies van die vorm y = cos ( θ + p )

Op dieselfde assestelsel, plot die volgende grafieke:

  1. a ( θ ) = cos ( θ - 90 )
  2. b ( θ ) = cos ( θ - 60 )
  3. c ( θ ) = cos θ
  4. d ( θ ) = cos ( θ + 90 )
  5. e ( θ ) = cos ( θ + 180 )

Gebruik jou resultate om die effek van p af te lei.

Jy sal vind dat die waarde van p affekteer die y -afsnit en die fase skuif van die grafiek. Soos in die geval van die sinus grafiek, positiewe waardes van p skuif die cosinus grafiek links, terwyl negatiewe p waardes skuif die grafiek regs.

Die verskillende eienskappe word opgesom in [link] .

Tabel wat die algemene vorm en posisie van grafieke van funksies in die vorm y = cos ( θ + p ) opsom. Die kurwe y = cos θ is geplot met die 'n stippellyn.
p > 0 p < 0

Definisie versameling en waarde versameling

Vir f ( θ ) = cos ( θ + p ) is die definisie versameling { θ : θ R } , omdat daar geen waarde is van θ R waarvoor f ( θ ) ongedefinieerd is nie.

Die waarde versameling van f ( θ ) = cos ( θ + p ) is { f ( θ ) : f ( θ ) [ - 1 , 1 ] } .

Afsnitte

Vir funksies van die vorm y = cos ( θ + p ) , word die metode om die afsnit met die y as te kry gegee.

Die y -afsnite word bereken as volg: stel θ = 0

y = cos ( θ + p ) y afsnit = cos ( 0 + p ) = cos ( p )

Funksies van die vorm y = tan ( θ + p )

In die vergelyking y = tan ( θ + p ) , is p 'n konstante en het verskeie effekte op die grafiek van die funksie. Die algemene vorm van grafieke van funksies in die vorm word gegee in [link] for the function f ( θ ) = tan ( θ + 30 ) .

Die grafiek van tan ( θ + 30 ) (vastelyn) en die grafiek van g ( θ ) = tan ( θ ) (stippellyn).

Funksies van die vorm y = tan ( θ + p )

Op dieselfde assestelsel, plot die volgende grafieke:

  1. a ( θ ) = tan ( θ - 90 )
  2. b ( θ ) = tan ( θ - 60 )
  3. c ( θ ) = tan θ
  4. d ( θ ) = tan ( θ + 60 )
  5. e ( θ ) = tan ( θ + 180 )

Gebruik jou resultate om die effek van p af te lei.

Jy behoort te vind dat die waarde van p affekteer weereens die y -afsnit en die fase skuif van die grafiek. Daar is 'n horisontale skuif na links indien p positief is en na regs indien p negatief is.

Die verskillende eienskappe word opgesom in [link] .

Tabel wat die algemene vorm en posisie van grafieke van funksies in die vorm y = tan ( θ + p ) opsom. Die kurwe y = tan ( θ ) word geplot met 'n stippellyn.
k > 0 k < 0

Definisie versameling en waade versameling

Vir f ( θ ) = tan ( θ + p ) is die definisie versameling van een tak { θ : θ ( - 90 - p , 90 - p } , omdat die funksie ongedefinieerd is vir θ = - 90 - p en θ = 90 - p .

Die waarde versameling van f ( θ ) = tan ( θ + p ) is { f ( θ ) : f ( θ ) ( - , ) } .

Afsnitte

Vir funksies van die vorm y = tan ( θ + p ) word die metode om die afsnitte met die y as te bereken gegee.

Die y -afsnit word as volg bereken: stel θ = 0

y = tan ( θ + p ) y afsnit = tan ( p )

Asimtote

Die grafiek van tan ( θ + p ) het asimtote, omdat soos θ + p 90 benader, benader tan ( θ + p ) oneindig. Daar is dus geen gedefinieerde waarde vir die funksie by die asimtoot waardes nie.

Funksies van verskillende vorms

Gebruik jou kennis van die effekte van p en k teken 'n rowwe skets van die volgende funksies, sonder om 'n tabel van waardes te gebruik.

  1. y = sin 3 x
  2. y = - cos 2 x
  3. y = tan 1 2 x
  4. y = sin ( x - 45 )
  5. y = cos ( x + 45 )
  6. y = tan ( x - 45 )
  7. y = 2 sin 2 x
  8. y = sin ( x + 30 ) + 1

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Source:  OpenStax, Siyavula textbooks: wiskunde (graad 11). OpenStax CNX. Sep 20, 2011 Download for free at http://cnx.org/content/col11339/1.4
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