Razones Trigonometricas

 

Nsbundc Glricd Rupnrelr hn Ilgtnrrny Muéc ‒  Xcddnr  Xcddnr Mrchl hnbeil

PC[LGNR XPEMLGLINXPE XPEMLGLINXPEBCR BCR

Icpc blgbnptucd hn dcs rczlgns tremlgliåtrebcs

 

Nsbundc Glricd Rupnrelr hn Ilgtnrrny Muéc ‒  Xcddnr  Xcddnr Mrchl hnbeil

snb  9 bsnb bsnb  9 btcg  9

dcs

rczlgns

`csebcs

slg

fepltngusc

 

bctntl chycbngtn fepltngusc   bctntl lpunstl

bctntl chycbngtn bctntl lpunstl

 

tremlglintrebcs sngl, blsngl

l

tcgmngtn, sn hn`n vnreaebcr qun dc bcdbudchlrc sn ngbungtrn ng nd

Augbelg Rngl 

sestnic

Augbelg Blsngl 

qun

vcg

c

trc`ckcr

(snxmnseicd l rchecd). Rnxcmnseicd sn ehngteaebc blg dc dntrc H ng dc pcrtn supnrelr hn dc pcgtcddc Pchecd sn ehngteaebc blg dc dntrc P  ng dc pcrtn supnrelr hn dc pcgtcddc. Zcrc sndnbbelgcr cdmugc hn dcs hls lprein;

RFEAX + RNX^Z U sndnbbelgc dc lpbelg Hnm pcrc snxcmnseicd l Pch pcrc rchecd

Augbelg Xcgmngtn 

 

Nsbundc Glricd Rupnrelr hn Ilgtnrrny Muéc ‒  Xcddnr  Xcddnr Mrchl hnbeil

^scghl dc bcdbudchlrc fcddcr;

c)  Rng 63º

`) sng 08º

n) sng >8º 2:― 

a) bls ( ) 

b) bls 2>º



h) tcg 8>º

m) tcg  ϊ  



PNRLD^BEÒG HN XPECGM^DLR PNBXCGM^DLR BLG PC[LGNR XPEMLGLINXPEBCR Ng nd semuengtn trecgmudl sn iunstrc blil sn hntnriegcg dcs rczlgns tremlgliåtrebcs ng ug treãgmudl rnbtãgmudl Bctntl chycbngtn ns nd dchl qun cyuhc c alricr nd ãgmudl

ΰ 

blg dc fepltngusc.

>

2 8

Bctntl lpunstl  ns nd dchl qun sn ngbungtrc arngtn cd ãgmudl.

γ 

Dc fepltngusc hnd treãgmudl rnbtãgmudl ns >

  9

B  F



9  

  9



Nd bctntl lpunstl blg rnspnbtl cd ãgmudl γ ns 2

  9

B  F

8

9   

  9

B  B   B 



9   8



9  



8



b  9   9     

  9

B 

F

8

9   

Nd bctntl lpunstl blg rnspnbtl cd ãgmudl   ns 8

  9

B 



9  

F



Nd bctntl chycbngtn blg rnspnbtl cd ãgmudl   ns 2

Nd bctntl chycbngtn blg rnspnbtl cd ãgmudl γ ns 8

  9

B 

  9   9

B 

8

B  

8

9      9

  





B 

  9

9   9   



9  

  B 





9 8 

 

Nsbundc Glricd Rupnrelr hn Ilgtnrrny Muéc ‒  Xcddnr  Xcddnr Mrchl hnbeil

Fcddcr dcs rczlgns tremlgliåtrebcs hn dls semuengtns treãgmudls;

 ΰ  1: =

 ΰ 

3:

0>

γ  

 ΰ 

γ  

20

6 30

>

 ΰ 

γ  

RLD^BELG HN XPECGM^DLR PNBXCGM^DLR BLG PC[LGNR XPEMLGLINXPEBCR XPEMLGLINXPEBCR Fcddcr ãgmudls utedezcghl dcs rczlgns tremlgliåtrebcs.

Dl preinrl ns l`snrvcr dc aemurc y blg dls hctls hchls, cgcdezcr quå rczòg tremlgliåtrebc ns dc chnbuchc pcrc uscr. Rn l`snrvc qun hn`nils fcddcr nd ãgmudl γ y qun gls hcg dls hctls hnd bctntl lpunstl c nstn ãgmudl y dc fepltngusc hnd treãgmudl, treãgmudl, sn hnhubn qun dc rczòg tremlgliåtrebc chnbuchc chnbuchc pcrc fcddcr fcddcr nd ãgmudl ns RNGL

  9

  

 

 

Nsbundc Glricd Rupnrelr hn Ilgtnrrny Muéc ‒  Xcddnr  Xcddnr Mrchl hnbeil

  9

2 >

 

  9 :.1 Cflrc cprnghnrnils blil fcddcr ãgmudls utedezcghl dcs rczlgns tremlgliåtrebcs. Xngnr ng bungtc qun dcs rczlgns utedezchcs pcrc fcddcr dls ãgmudls slg RNGL, BLRNGL U XCGMNGXN. Nstl sn rncdezc plrqun slg dcs rczlgns qun sn ngbungtrcg ng dc bcdbudchlrc. Zcsl 3; hnspnkcr nd ãgmudl

9

:.1 

 

Blil dc rczòg RNGL nstc ng nd hngliegchlr y gnbnsetcils utedezcrdc dc su`eils cd guinrchlr blg nxplgngtn gnmctevl

 9 ∐ (:.1)  Ng dc bcdbudchlrc sn hnscrrlddc hn dc semuengtn alric

RFEAX +RNG +(:.1)

 

Nsbundc Glricd Rupnrelr hn Ilgtnrrny Muéc ‒  Xcddnr  Xcddnr Mrchl hnbeil

 9 ∐ (:.1)  Nd ãgmudl qun l`tengng ns ng snxcmnseicd plr nstn iltevl vnreaebcr qun dc bcdbudchlrc sn ngbungtrn ng nstn sestnic

;  9 21.6156 …  Zcrc vnr nd ãgmudl ng alric blipdnkc sldl hn`ng lpreier ng dc bcdbudchlrc b cdbudchlrc

   ;  9 21º >0‰  33.12"  Hn dc iesic alric sn rncdezc blg dcs rczlgns BLRNGL U XCGMNGXN. Nknrbebels

Fcddcr dls ãgmudls hn dls semuengtns treãgmudls blg dc rczòg tremlgliåtrebc chnbuchc.

 ΰ  1: 3:

Fcddcr nd ãgmudl  ΰ 

Fcddcr nd ãgmudl  ΰ 

 ΰ  20

6

30

0>

>

= Fcddcr nd ãgmudl   

γ  

Fcddcr nd ãgmudl   

γ