Obj. 19 Graphs of Sine and Cosine (Presentation)
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Transcript of Obj. 19 Graphs of Sine and Cosine (Presentation)
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8/3/2019 Obj. 19 Graphs of Sine and Cosine (Presentation)
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Kni, :3 D~jqfu ko Ucl` jlh Ekucl`
Plcx 0 X~cdklkb`x~ce jlh Ec~epgj~ Oplexcklu
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8/3/2019 Obj. 19 Graphs of Sine and Cosine (Presentation)
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Ekle`qxu jlh Kni`excv`u
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 efjld`u cl
Jbqgcxph`
Q`~ckh
_`~xcejg x~jlugjxckl
Qfju` ufcox
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8/3/2019 Obj. 19 Graphs of Sine and Cosine (Presentation)
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D~jqfcld xf` Ucl` Oplexckl
N`ejpu` xf` ucl` cu j ec~epgj~oplexckl' tfcg` ejl n`
jls lpbn`~ &qkucxcv` k~ l`djxcv`#' xf` vjgp` ko ucl klgs dk`u 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~~`uqklhcld ekk~hcljx`u
o~kb xf` plcx ec~eg` ju kp~s"ekk~hcljx`,
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8/3/2019 Obj. 19 Graphs of Sine and Cosine (Presentation)
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D~jqfcld xf` Ucl` Oplexckl
Co t` d~jqf xf`u` vjgp`u kl j ekk~hcljx` qgjl`' t` ejl
u`` fkt xfcu oplexckl ep~v`u9
Xf` m`s xk d~jqfcld xf` ucl` oplexckl cu xfjx cx clegph`u
xf` qkclx&1' 1#,
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8/3/2019 Obj. 19 Graphs of Sine and Cosine (Presentation)
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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' :#,
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8/3/2019 Obj. 19 Graphs of Sine and Cosine (Presentation)
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Efjldcld xf` Njuce D~jqf
Jbqgcxph` h`ue~cn`u 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 vjgp`u,
Q`~ckhh`ue~cn`u xf` eseg` ko xf` d~jqffkt gkld cx
xjm`u ok~ xf` d~jqf xk uxj~x ~`q`jxcld,
Xf` q`~ckh ko xf` ucl` k~ ekucl` cu ,
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8/3/2019 Obj. 19 Graphs of Sine and Cosine (Presentation)
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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
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8/3/2019 Obj. 19 Graphs of Sine and Cosine (Presentation)
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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'~`uq`excv`gs' `e`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
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8/3/2019 Obj. 19 Graphs of Sine and Cosine (Presentation)
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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,
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8/3/2019 Obj. 19 Graphs of Sine and Cosine (Presentation)
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Q`~ckh
Ok~ n < 1' xf` d~jqf kos2 ucl nvtcgg ~`u`bng` xfjx ko
s2 uclv' npx tcxf q`~ckh , Jguk' xf` d~jqf ko
s2 eku nvtcgg ~`u`bng` xfjx kos2 ekuv' npx tcxf q`~ckh
Xk ejgepgjx` xf` q`~ckh ko j oplexckl' upnuxcxpx` xf`
ek`oocec`lx kovcl ok~ n jlh ~`hpe`,
n
n
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8/3/2019 Obj. 19 Graphs of Sine and Cosine (Presentation)
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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
:
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8/3/2019 Obj. 19 Graphs of Sine and Cosine (Presentation)
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Um`xefcld j Ec~epgj~ D~jqf
@jbqg`9 Um`xef xf` d~jqf ko kv`~ kl`
q`~ckh,
2 ucl
vs
v 1 > 5 8
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v
ucl>
v
>ucl>v
1
1
1
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1
1
5
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1
1
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8/3/2019 Obj. 19 Graphs of Sine and Cosine (Presentation)
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Um`xefcld j Ec~epgj~ D~jqf
@jbqg`9 Um`xef xf` d~jqf ko kv`~ kl`
q`~ckh,
Lkxce` xfjx tf`l j cu l`djxcv`' xf` d~jqf cu ~`og`ex`h
jnkpx xf`v"jcu,
2 >ucl>
vs
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8/3/2019 Obj. 19 Graphs of Sine and Cosine (Presentation)
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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
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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` vjgp`u ju n`ok~`' k~ skp ejl um`xef xf`
ux~`xef`h+ekbq~`uu`h qj~`lx d~jqf jlh x~jlugjx` cx
jeek~hcld xk e jlh h,
Xf` u`eklh b`xfkh cu q~knjngs xf` `juc`ux xk hk kle`skp j~` ekbok~xjng` tcxf xf` njuce d~jqfu,
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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
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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
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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
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Fkb`tk~m Ekgg`d` Jgd`n~j
Qjd` 0359 :0' :?' :3' >5' 58 FT9 :?' >1' 58' 8>' 88