<< Chapter < Page Chapter >> Page >
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

what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
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.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
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
Do you know which machine is used to that process?
s.
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
how to synthesize TiO2 nanoparticles by chemical methods
Zubear
what's the program
Jordan
?
Jordan
what chemical
Jordan
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
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 10) [caps]. OpenStax CNX. Aug 04, 2011 Download for free at http://cnx.org/content/col11328/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Siyavula textbooks: wiskunde (graad 10) [caps]' conversation and receive update notifications?

Ask