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Cng thc l-ng gic I. Gi tr cc hm s l-ng gi c ca cc cung (gc ) c bit

00 300 450 00 900 1200 1350 1500 1800 3600Gc

Hslg0

6

4

3

2

3

2

4

3

6

5

2

sin 0

2

1

2

2

2

3

1

2

3

2

2

2

1

0 0

cos 123

22

21 0

21

22

23 -1 1

tg 0

3

3

1 3 kx 3 -1

3

3

0 0

cotg kx 3 1

3

3

0

3

3

-1 3 kx kx

Ta nn s dng -ng trn l-ng gic ghi nh cc gi tr c bitII. Quan h l-ng gic ca cc c ung (gc) c lin quan c bit

1. Cung i nhau:( Cos i) 2. Cung b nhau(Sin b)cos( ) cossin( ) sin

( )

cot ( ) cot

tg tg

g g

cos( ) cos

sin( ) sin

( )

cot ( ) cot

tg tg

g g

3. Cung ph nhau: (ph cho) 4. Cung hn km cos( ) sin

2

sin( ) cos2

( )2

cot ( ) t2

tg cotg

g g

cos( ) cos

sin( ) sin( )

cot ( ) cot

tg tg

g g

5.Cung hn km2

6. Cung hn km 2k

cos( ) sin2

sin( ) cos2

( )2

cot ( ) t2

tg cotg

g g

sin( 2 ) sin

cos( 2 ) cos

( 2 )

cot ( 2 ) cot

k

k

tg k tg

k g

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III. Cng thc l-ng gic 1. Cng thc l-ng gic c bn 2 2

2

2

cos sin 1

11 tg =

cos

2

2

11 cotg =

sin

tg . cotg = 1

2. Cng thc cngcos( ) cos .cos sin .sin

cos( ) cos .cos sin .sin

sin( ) sin .cos sin .cos

sin( ) sin .cos sin .cos

tg +tgtg( + ) =

1 .

tg tgtg( ) =

1 .

tg tg

tg tg

3. Cng thc nhn i

2

sin 2 2sin .cos

22

1

tgtg

tg

2 2

2

2

cos 2 cos sin

2cos 1

1 2sin

4 Cng thc nhn ba(tham kho)3

3

cos3 4cos 3cos

sin 3 3sin 4sin

5. Cng thc h bc:1

sin .cos sin 22

x x 21 cos 2

cos2

2 1 cos 2sin2

2 1 cos 2

1 cos 2tg

6.Cng thc tnh sin ,cos ,tg theo2

t tg

22

2

2 1

2;

1

1cos;

1

2sin

t

ttg

t

t

t

t

7. Cng thc bin i tch thnh tng

1cos .cos cos( ) cos( )

2

1sin .sin cos( ) cos( )

2

1sin .cos sin( ) sin( )

2

8. Cng thc bin i tng thnh tchcos cos 2cos .cos

2 2

cos cos 2sin .sin2 2

sin sin 2sin .cos2 2

sin sin 2cos .sin2 2

2

2

sin( )

cos cos

sin( )

cos cos

1 cos 2cos2

1 cos 2sin2

tg tg

tg tg

aa

aa

4

cos33coscos3

4

3sinsin3sin 3