obj. 19 graphs of sine and cosine (presentation)

8/3/2019 Obj. 19 Graphs of Sine and Cosine (Presentation)

1/19

Kni, :3 D~jqfu ko Ucl` jlh Ekucl`

Plcx 0 X~cdklkb`x~ce jlh Ec~epgj~ Oplexcklu


2/19

Ekle`qxu jlh Knièxcvù

D~jqfu ko xf` Ucl` jlh Ekucl` Oplexcklu &Kni, %:3#

N` jng` xk d~jqf xf` ucl` jlh ekucl` oplexcklu kl xf`clx`~vjg ' R

N` jng` xk ch`lxcos fkt xf` d~jqfu ko xf` ucl` jlh

ekucl` efjld` hp` xk efjldù cl

Jbqgcxph`

Q`~ckh

_`~xcejg x~jlugjxckl

Qfju` ufcox


3/19

D~jqfcld xf` Ucl` Oplexckl

Nèjpu` xf` ucl` cu j ec~epgj~oplexckl' tfcg` ejl n`

jls lpbn`~ &qkucxcv` k~ l`djxcv`#' xf` vjgp` ko ucl klgs dkù o~kb : xk :, &Cx cu jguk ekluch`~`h jq`~ckhce

oplexckl,#

Xk d~jqf j ec~epgj~ oplexckl' t` ejl xjm` xf` jldg` ju

kp~v"ekk~hcljx` jlh xf` ek~~ùqklhcld ekk~hcljxù

o~kb xf` plcx ec~eg` ju kp~s"ekk~hcljx`,


4/19

D~jqfcld xf` Ucl` Oplexckl

Co t` d~jqf xfù` vjgpù kl j ekk~hcljx` qgjl`' t` ejl

u`` fkt xfcu oplexckl ep~vù9

Xf` m`s xk d~jqfcld xf` ucl` oplexckl cu xfjx cx clegphù

xf` qkclx&1' 1#,


5/19

D~jqfcld xf` Ekucl` Oplexckl

Xf` ekucl` oplexckl cu v`~s ucbcgj~ xk xf` ucl`, G`xu gkkm

jx j d~jqf ko cx9

Xf` m`s xk d~jqfcld xf` ekucl` oplexckl cu xfjx cx

clegph`u xf` qkclx&1' :#,


6/19

Efjldcld xf` Njuce D~jqf

Jbqgcxph` hùe~cnù fkt xf` njuce d~jqf cu efjld`h

v`~xcejggs &xjgg`~ k~ ufk~x`~#, Xf` jbqgcxph` ko j q`~ckhceoplexckl cu fjgo xf` hcoo`~`le` n`xt``l xf` bjcbpb

jlh bclcbpb vjgpù,

Q`~ckhhùe~cnù xf` eseg` ko xf` d~jqffkt gkld cx

xjmù ok~ xf` d~jqf xk uxj~x ~`q`jxcld,

Xf` q`~ckh ko xf` ucl` k~ ekucl` cu ,


7/19

Jbqgcxph`

Ekbqj~` xf` d~jqfu ko jlh

Lkxce` xfjx nkxf d~jqfu e~kuu xf`v"jcu jx xf` ujb`

qgje`u jlh xfjx nkxf d~jqfu q`jm jx xf` ujb` qgje`u,

2 ucls v 2 ucls v


8/19

Jbqgcxph`

Xf` d~jqf kos2 j uclvk~s2 j ekuv' tcxf j 1' tcgg

fjv` xf` ujb` ufjq` ju xf` d~jqf kos2 uclvk~s2 ekuv'~ùqèxcv`gs' è`qx tcxf xf` ~jld` wjw' wjwR, Xf`

jbqgcxph` cu wjw,

@jbqg`9 Tfjx cu xf` jbqgcxph` ko ; Tfjx cu

xf` ~jld` ko xf` d~jqf;

2 :eku5

s v

:

Jbqgcxph`9 5

: :

^jld`9 '5 5


9/19

Q`~ckh

Ekbqj~` xf` d~jqfu kos2 ekuvjlhs2 eku v,

Xf` xtk d~jqfu fjv` xf` ujb` f`cdfx' npx xf` u`eklh

d~jqf cu ekbq~`uu`h,


10/19

Q`~ckh

Ok~ n < 1' xf` d~jqf kos2 ucl nvtcgg ~ù`bng` xfjx ko

s2 uclv' npx tcxf q`~ckh , Jguk' xf` d~jqf ko

s2 eku nvtcgg ~ù`bng` xfjx kos2 ekuv' npx tcxf q`~ckh

Xk ejgepgjx` xf` q`~ckh ko j oplexckl' upnuxcxpx` xf`

ekòocec`lx kovcl ok~ n jlh ~`hpe`,

n

n


11/19

Um`xefcld j Ec~epgj~ D~jqf

@jbqg`9 Um`xef xf` d~jqf ko kv`~ kl`

q`~ckh,

Xf` ek`oocec`lx kovcu ' uk xf` q`~ckh cu

Lkt' hcvch` xf` clx`~vjg 1' 8R clxk okp~ `zpjg qj~xu jlh

`vjgpjx` xf` oplexckl jx xfku` vjgp`u,

2 ucl

vs

:

2

8

:


12/19



q`~ckh,

2 ucl

vs

v 1 > 5 8

>

v

ucl>

v

>ucl>v

1

1

1

>

:

>

1

1

5

>

:

>

>

1

1


13/19



q`~ckh,

Lkxce` xfjx tf`l j cu l`djxcv`' xf` d~jqf cu ~`og`ex`h

jnkpx xf`v"jcu,

2 >ucl>

vs


14/19

X~jlugjxcld Ucl` jlh Ekucl`

T` fjv` u``l tfjx xf` d~jqf kos2 j ucl nvgkkmu gcm`,

L`x' t` ejl ufcox xf` d~jqf v`~xcejggs jlh+k~fk~cyklxjggs,

Xf` opgg ok~b ko xf` ucl` oplexckl cu

e joo`exu xf` v`~xcejg qkucxckl ko xf` d~jqf, J qkucxcv`

e ufcoxu xf` d~jqf e plcxu pq' jlh j l`djxcv` e ufcoxu

xf` d~jqf e plcxu hktl,

hufcoxu xf` d~jqf fk~cyklxjggs, &v- h# ufcoxu xf` d~jqfhplcxu xk xf` g`ox' jlh &v h# ufcoxu xf` d~jqf hplcxu

xk xf` ~cdfx,

& #2 - ucls e j n v h


15/19

X~jlugjxcld Ucl` jlh Ekucl`

Tcxf ec~epgj~ oplexcklu' j fk~cyklxjg x~jlugjxckl cu ejgg`h

jqfju` ufcox, Xf` qfju` ufcox cu xf` jnukgpx` vjgp` koh,

Xk um`xef xf` x~jlugjx`h d~jqf' skp ejl `cxf`~ hcvch` xf`

clx`~vjg clxk okp~ qj~xu &`cdfx qj~xu ok~ xtk q`~ckhu# jlh

efj~x xf` vjgpù ju nòk~`' k~ skp ejl um`xef xf`

ux~`xef`h+ekbq~ùu`h qj~`lx d~jqf jlh x~jlugjx` cx

jeek~hcld xk e jlh h,

Xf` uèklh b`xfkh cu q~knjngs xf` `jucùx xk hk kle`skp j~` ekbok~xjng` tcxf xf` njuce d~jqfu,


16/19

D~jqfcld Ucl` jlh Ekucl` @jbqg`9 D~jqf kv`~ kl` q`~ckh,

2 -5eku

8s v

2 2 2 25' :' 1' xk xf` g`ox

8j n e h


17/19

D~jqfcld Ucl` jlh Ekucl` @jbqg`9 D~jqf kv`~ xtk q`~ckhu,

Xk oclh xf` vjgp` kon' t` tcgg fjv` xk ojexk~ kpx xf` 8 cl

o~klx ko xf`v9

& #2 - - : >ucl 8s v

2 - -

: >ucl8 8s v

2 2 2 2>' 8' :' xk xf` g`ox

8j n e h

2 2> >Q`~ckh98 >n


18/19

D~jqfcld Ucl` jlh Ekucl` @jbqg`9 D~jqf kv`~ xtk q`~ckhu,& #2 - - : >ucl 8s v

2 - -: >ucl8

8s v

2 2 2 2 >' 8' :'

8

j n e h

Q`~ckh9

>


19/19

Fkb`tk~m Ekgg`d` Jgd`n~j

Qjd` 0359 :0' :?' :3' >5' 58 FT9 :?' >1' 58' 8>' 88

obj. 19 graphs of sine and cosine (presentation)

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