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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.

Questions & Answers

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
hi
Loga
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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