<< Chapter < Page Chapter >> Page >

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

Questions & Answers

Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
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
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Berger describes sociologists as concerned with
Mueller Reply
Got questions? Join the online conversation and get instant answers!
QuizOver.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Siyavula textbooks: wiskunde (graad 11). OpenStax CNX. Sep 20, 2011 Download for free at http://cnx.org/content/col11339/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Siyavula textbooks: wiskunde (graad 11)' conversation and receive update notifications?

Ask