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θ 0 30 60 90 120 150
cos θ
θ 180 210 240 270 300 330 360
cos θ

Laat ons terugkyk na ons waardes vir cos θ .

θ 0 30 45 60 90 180
cos θ 1 3 2 1 2 1 2 0 - 1

As jy noukeurig kyk, sal jy oplet dat die cosinus van 'n hoek θ dieselfde is as die sinus van die hoek ( 90 - θ ). Neem byvoorbeeld,

cos 60 = 1 2 = sin 30 = sin ( 90 - 60 )

Dit wys ons dat ten einde 'n cosinusgrafiek te skep, al wat ons hoef te doen is om die sinusgrafiek 90 na links te skuif. die grafiek van cos θ word gewys in [link] . As die cosinusgrafiek eenvoudig 'n geskuifde sinusgrafiek is, sal dit dieselfde periode en amplitude as die sinuskurwe hê.

Grafiek van cos θ

Funksies in die vorm y = a cos ( x ) + q

In die vergelyking, y = a cos ( x ) + q . a and q is konstantes en het verskillende invloede op die grafiek van die funksie. Die algemene vorm van die grafieke van hierdie soort funksies word getoon in [link] vir die funksie f ( θ ) = 2 cos θ + 3 .

Grafiek van f ( θ ) = 2 cos θ + 3

Funksies van die vorm y = a cos ( θ ) + q :

  1. Op dieselfde stel asse, trek die volgende grafieke:
    1. a ( θ ) = cos θ - 2
    2. b ( θ ) = cos θ - 1
    3. c ( θ ) = cos θ
    4. d ( θ ) = cos θ + 1
    5. e ( θ ) = cos θ + 2
    Gebruik jou resultate om die invloed van q af te lei.
  2. Op dieselfde stel asse, trek die volgende grafieke:
    1. f ( θ ) = - 2 · cos θ
    2. g ( θ ) = - 1 · cos θ
    3. h ( θ ) = 0 · cos θ
    4. j ( θ ) = 1 · cos θ
    5. k ( θ ) = 2 · cos θ
    Gebruik jou resultate om die invloed van a af te lei.

Ons vind dat die waarde van a die amplitude van die cosinusgrafiek op dieselfde manier beïnvloed as wat dit vir die sinusgrafiek gedoen het.

Verandering in die waarde van q sal die die cosinusgrafiek op dieselfde manier skuif as wat dit vir die sinusgrafiek gedoen het.

Die verskillende eienskappe word opgesom in [link] .

Tabel wat die algemene vorms en posisies van grafieke en funksies in die vorm y = a cos ( x ) + q opsom
a > 0 a < 0
q > 0
q < 0

Gebied en terrein

Vir f ( θ ) = a cos ( θ ) + q , is die gebied { θ : θ R } want daar is geen waarde van θ R waarvoor f ( θ ) ongedefinieërd is nie.

Dit is maklik om te sien dat die terrein van f ( θ ) dieselfde sal wees as die terrein van a sin ( θ ) + q . Dit is omdat die maksimum en minimumwaardes van a cos ( θ ) + q dieselfde is as die maksimum en minimumwaardes van a sin ( θ ) + q .

Snypunte

Die y -afsnit van f ( θ ) = a cos ( x ) + q word bereken op dieselfde wyse as vir sinus.

y i n t = f ( 0 ) = a cos ( 0 ) + q = a ( 1 ) + q = a + q

Vergelyking van die grafieke van sin θ En cos θ

Die grafiek van cos θ (soliede lyn) en die grafiek van sin θ (stippellyn)

Let daarop dat die twee grafieke baie eenders lyk. Beide ossilleer op en af rondom die x -as soos wat jy beweeg langs die as. Die afstande tussen die pieke van die twee grafieke is dieselfde en is konstant vir elke grafiek. Die hoogte van elke piek en die diepte van elke trog is dieselfde.

Die enigste verskil is dat die sin grafiek skuif 'n bietjie na regs ten opsigte van die cos grafiek, met 90 . Dit beteken dat as ons die hele cos grafiek 90 na regs skuif, sal dit perfek oorvleul met die sin grafiek. Jy kan ook die sin grafiek 90 na links skuif en dan sal dit perfek oorvleul met die cos grafiek. Dit beteken dat:

sin θ = cos ( θ - 90 ) ( skuif die cos grafiek na die regterkant ) en cos θ = sin ( θ + 90 ) ( skuif die sin grafiek na die linkerkant )

Grafiek van tan θ

Grafiek van tan θ

Voltooi die volgende tabel, gebruik jou sakrekenaar en bereken die waardes korrek tot 1 desimale plek. Stip dan die waardes met tan θ op die y -as en θ op die x -as.

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Mostly, they use nano carbon for electronics and for materials to be strengthened.
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In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
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Source:  OpenStax, Siyavula textbooks: wiskunde (graad 10) [caps]. OpenStax CNX. Aug 04, 2011 Download for free at http://cnx.org/content/col11328/1.4
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