MT VI CCH NH CC CNG THC LNG GIC

MT VI CCH NH CC CNG THC LNG GIC

Lng gic l mt phn mn quan trng trong chng trnh ton ph thng, n theo chn cc bn t bi ton gii tam gic, gii phng trnh lng gic, n tnh o hm tch phn, s phc . hc tt mn hc ny, mt yu cu quan trng l phi thuc c cc cng thc lng gic .C bt mi gt nn h , phi khng cc bn ?

Bi vit nh ny chia s vi cc bn nhng kinh nghim nh cc cng thc lng gic ca ti, mt trong nhng hnh hnh trang m ti lun mang theo trn con ng hc ton ca mnh .

1. Du ca cc gi tr lng gic (GTLG) :

Cc bn nn bit trong gc vung (gc phn t) th nht, mi GTLG u mang du dng (+) , di chuyn du + ny theo chiu dc , ta c du ca cos, theo chiu ngang ta c du sin v nu di chuyn cho i xung gc phn t th 3 ta c du ca tan v cotan (cn trong nhng gc vung cn li d nhin du s l m !). Th nn ghi nh du ca cc hm s lng gic ta c: cos dc, sin ngang, tan - cotan cho.2)Gi tr LG ca cc gc c bit cc bn c th dng my tnh, tuy nhin nu khng c my tnh th ta vn nh c mt cch d dng nh cch chia nhm nh sau:

Trc ht cn nh mt cu thn ch quen thuc m ta bit t cp 2 sin i hc, cos khng ham (khng h) tan on kt cotan kt on.Vi cc GTLG ca gc ta c na hnh vung c cnh bng 1 ( cng chnh l tam gic vung cn c cnh bng 1) d thy khi ng cho ca hnh vung ny l . T ta c ngay ,

Cn vi cc GTLG ca cc gc 300 , 600 , ta dng na tam gic u c cnh bng 1. Ta c: ,.

Cc gc 00, 900 ,1800 th ta li dng n na ng trn lng gic .

Chng hn ta d dng suy ra t ta ca im

A(-1; 0) (khi ta dng cu sin ng , cos nm nh vi M nm trn ng trn hay na ng trn lng gic ; gc (Ox, OM) = a.Mt iu na l nhiu khi ta ch cn nh cc gi tr ca sin v cos thi cn tan v cotan ta suy ngay ra c nh h thc quen thuc.

,

, thm ch ch cn nh i vi tan v tana v cota

l 2 s nghch o ca nhau .

* Khi ni sin tng cos gim th ta c th hiu l : trong gc vung th nht , hm sin tng (ng bin) , cn hm cos gim (Nghch bin) khi gc tng t 0 n 900 .

3) GTLG ca cc gc c lin quan c bit: Chc chng ta u bit n cu quen thuc cos i, sin b, ph cho, khc tan cotan cng cn phi hiu k hn ngha ca cu ny cc GTLG c nhc n th bng nhau cn nu khng c nhc n th chng i nhau ! .

V cch nh cc lin quan c bit ny, ti hc t thy gio dy ton ca ti. Cc bn cng c cho vui nh :* Lin quan i (a v a)

Nu 2 gc i nhau

Cos ca chng bng nhau

Sin,tan cotan i

Hy vit vo mau mau .

* Lin quan b (a v - a)

Nu hai gc m b

Cos phi thm du tr

Tan cotan cng vy (*)

Sin bng nhau r cha ?

* Hn km mt (a v a + )

Nu hn km mt

Chuyn c kh g

Sin cos i du i

Tan cotan vn vy

* Hn km mt vung (a v a + )

Nu hn km mt vung ()

Chuyn ny kh khn hn

Sin ln bng cos nh

cos ln bng tr sin con .

* Lin quan ph (a v - a )

Ph nhau th d gh

Sin ny bng cos kia

Tan ny bng cotan n

Nh khng h 11C ?

(By gi lp hc ton ghi l A1, A2nn kh gieo vn qu !), tuy nhin cc bn cng nn nh rng : Mun bin cos thnh sin v ngc li th hy dng lin quan ph.

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3 (Cc bn c th kim tra li cc lin quan c bit ny bng cng thc cng .V d hn km 1 vung , nu nh c cc cng thc ny s rt tt cho bn y

4) Cc cng thc cng :

* i vi sin v cos :Cos th cos cos sin sin

Sin th sin cos cos sin kh g

Bn i hy nh hy ghi

Cos thi i du sin th gi nguyn.

Hoc sin cng du , khc loi cos cng loi , khc du

* Cng thc cng tan :

Tan ca tng 2 tng cao rng

Trn thng tng l tng hai tan

Di h tng s 1 ngang tng

Dm tr i tch tan tan oai hng .5) Cc cng thc nhn i, nhn 3, h bc :

Cn bit rng chng c sinh ra t cng thc cng (vy nn nu qun cng thc nhn i , nhn ba th ta c th m li d dng nh cng thc cng ).

Cng thc nhn 3 l mt trong cc cng thc quan trng m bn cn phi nh nu mun lm c bi phng trnh lng gic thi i hc .Vy nh th no y ? Ring ti , ti li dng cu sin tng, cos gim quan st cng thc ta thy :

+) sin ch biu th qua sin cos ch biu th qua cos

+) S m ca sin (t 1 n 3)cng nh h s (t 3 n 4)tng t tri qua phi, cn cos th c m v h s t tri qua phi u gim, cn gia vn l du tr (-), bn xem li nh:

.

6) Cc cng thc bin i :

* Cng thc bin i tng thnh tch

Nu bn chu kh th cng thy c rng , chng cng c sinh ra t cng thc cng .Cn cch nh ? chc chng ta u lm quen vi Bi th sau : Sin cng sin bng 2 sin cosSin tr sin bng 2 cos sinCos cng cos bng 2 cos cos

Cos tr cos bng tr 2 sin sin

V tri l sin cos ca 2 gc a, b cn v phi l sin cos na tng , na hiu 2 gc .

* Cng thc bin i tch thnh tng

trn l cch nh cng thc bin i tng thnh tch, mun c cng thc tch thnh tng th ch cn vit ngc li, khi ta thy rng tch cos cos bngcos tng + cos hiu, tch sin sin bng cos hiu -cos tng (hoc bng trcos tng - cos hiu) tch sin cos bngsin tng + sin hiu. nh c cng khng kh lm, phi khng cc bn ?* Mt vi ch khi vn dng cc cng thc lng gic :

Phi vn dng chiu ngc ca cng thc v phi bin i cng thc trc khi s dng.V d: , ,

, , ..

gii phng trnh lng gic phi c k nng bin i tng thnh tch, ngc li nhiu bi tm nguyn hm hay tnh tch phn li i hi chng ta phi bit tch hay bin i tch thnh tng.

Nhiu cng thc lin quan n cos thng c du cng cn sin th c du tr . V d: Cng thc h bc

;

;

Mt s biu thc quen nu cc bn v bit c cch bin i cng s rt c ch cho chng ta trong khi i bin , h bc hay thc hin cc php bin i khc . Chng hn nh:

Cc bn thn mn !Trn y l nhng kinh nghim nh cng thc lng gic ca bn thn ti cng vi nhng iu ti hc c ca thy ti, bn ti v c t hc sinh ca ti. Rt mong nhng kinh nghim gip ch c cho cc bn, d ch l mt phn nh b .

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