C¸c c«ng thøc c¬ b¶n :a) sin2x + cos2x = 1 b) tgx.cotgx = 1

c) tgx = d) cotgx =

e) = 1 + tg2x f) = 1 + cotg2x

Baøi taäp:

Baøi taäp 1: Ñoåi ra ñôn vò coøn laïi: 2700; 5400 ; 7500 ;4050 ; 11400; .

Baøi taäp 2: Cho bk cuûa moät ñtroøn laø R = 5 cm. Haõy tìm ñoä daøi cuûa caùc cung treân ñtroøn coù soá ño laø: 1; 1,5; 9000;8100

Baøi taäp 3: Cho moät ñtroøn coù baùn kính R = 8cm. Haõy tìm soá ño cuûa caùc cung coù ñoä daøi sau: 4cm, 8cm, 45cm.Baøi taäp 4: Bieåu dieãn caùc cung sau leân ñöôøng troøn löôïng giaùc. Trong caùc ñieåm ngoïn cuûa caùc cung ñoù nhöõng ñieåm naøo truøng nhau? Giaûi thích.

Baøi taäp 5: Treân ñöôøng troøn löôïng giaùc xaùc ñònh nhöõng ñieåm ngoïn cuûa nhöõng

hoï sau:

Baøi taäp:

Bài 1: Rót gän hay ®¬n gi¶n c¸c biÓu thøc :

a) cos2x + cos2x.tg2x b) sin2x.cotg2x + sin2x c)

d) e)

f) g)

Bµi 2: Rót gän biÓu thøc :

A = víi 0 < a <

B = víi < a <

C = víi 0 < a <

D = víi < a <

Bµi 3: Chøng minh c¸c ®¼ng thøc sau :

a) b)

c) d)

e) f)

g) h)

i) j)

k)

l) sin4a + cos4a = 1 – 2sin2a.cos2a m) sin6a + cos6a = 1 – 3.sin2a.cos2a

Bµi 4: TÝnh gi¸ trÞ cña c¸c hµm sè lîng gi¸c kh¸c biÕt

a) sinx = vaâ < x < b) tgx = 3 vaâ < x <

c) cotg15O = 2+ d) tgx = -1

Bµi 5: Cho tgx = 3 . TÝnh sè trÞ cña c¸c biÓu thøc sau :

A = B =

B = C =

E = F = sin4x + cos4x

G = sin6x – cos6x H = sinx.cosx –cos2x

Bµi 6: Cho sina + cosa = . TÝnh sè trÞ c¸c biÓu thøc :P = sina.cosa Q = sin4a + cos4a R = sin3a + cos3a S = sin5a + cos5a T = tg2a + cotg2a U = cotg3a + tg3a

Bµi 7: Cho tga + cotga = 3. TÝnh A = tga – cotga B = tg2a – cotg2a C = tg2a + cotg2a

D = tg4a + cotg4a E = tg3a + cotg3a F =

Bµi 8: Chøng minh :

a) =

b) = n Z+

c) sin2a.tga + cos2a.cotga + 2sina.cosa = tga + cotga

d) tga.tgb = e)

f) cotg2a.cotg2b – = 1

g)

h)

Bµi 9: Chûáng minh caác biïíu thûác sau àöåc lêåp vúái caác biïën x ; y , z , t . . . (khöng phuå thuöåc vaâo x ; y; . . )

A = 2(cos6x + sin6x) – 3(cos4x + sin4x) B = - (1 + tg2x)2

C = + sinx.cosx D =

E = 3(sin8x – cos8x) + 4(cos6x - 2sin6x) + 6sin4xF = 2(sin4x + cos4x + sin2x.cos2x)2 – sin8x – cos8x

Bµi 10: T×m tÊt c¶ c¸c gi¸ trÞ tham sè m ®Ó biÓu thøc sau ®©y kh«ng phô thuéc vµo x P = cos6x + sin6x + ( m – 1)sin2x.cos2x

Q = m(sin4x + cos4x) + 4(m + 1)sin2x.cos2x + sin6x + cos6x R = S = m(sin8x – cos8x) + 4(2sin6x – cos6x) – nsin4x

GOÁC VAÂ CUNG LIÏN KÏËT(cos àöëi ; sin buâ ; phuå cheáo ; tg & cotg sai )

Cung àöëi : a vaâ (- a ) cos(- a) = cosa ; sin(- a) = sina ;

tg(- a) = tga ; cotg(- a) = cotga

Cung buâ : a vaâ ( - a ) sin(- a) = sina ; cos(- a) = - cosa ;

tg(- a) = - tga ; cotg(- a) = - cotga

Cung phuå : a vaâ ( - a)

sin( - a) = cosa ; cos( - a) = sina ;

tg( - a) = cotga ; cotg( - a) = tga

Cung sai : a vµ ( + a) tg(+ a) = tga ; cotg(+ a) = cotga ;

sin(+ a) = -sina ; cos(+ a) = -cosa

GHI CHUÁ : sin(a ) = –sina ; cos(a ) = –cosa tg(a ) = tga ; cotg(a ) = cotga

Khi boã möåt thò tg vaâ cotg khöng àöíi dêëu ; sin vaâ cos àöíi dêëu

Bµi 11: TÝnh gi¸ trÞ cña :A = tg10O.tg20Otg30O.tg40O.tg50O.tg60O.tg70O.tg80O

B = cotg1O.cotg2O.cotg3O. . . cotg87O.cotg88O.cotg89O

C = cos10O + cos20O + cos30O + . . . . . . + cos150O + cos160O + cos170O

D = sin210O +sin220O +sin230 + . . . +sin2150O +sin2160O +sin2170O + sin2180o

E = tg20O + tg40O + tg60O + tg80O + . . .+ tg160O + tg180O

F = sin825O.cos(-15O) + cos75O.sin(-555O) + tg155O.cotg245O

G = H=

H= I =

J=

K =

L = sin( - a) - cos( - a) + cotg(2 - a) + tg( - a)