TRAN VINH

TAP

MOT

NHA XUAT BAN HA NOI



TRAN VINH

^

^

>.

THIET KE BAI GIANG
DAI SO VA GIAI TICH

/\

/\

NANG CAO - TAP MOT

NHA XUAT BAN HA NO!


Thiet kebai giang

giang mon Toan ldp 11.
Bg sach gom, 8 cuon:
Thiet kebdi gidng Hinh hoc 11:2 tap
Thiei kebdi gidng Dgi sdvd Gidi tich 11:2 tap
Thiit kebdi gidng Hinh hoc 11 ndng cao: 2 tap
Thiit kebdi gidng Dgi sdvd Gidi tich 11 ndng cao: 2 tap
Day la b6 sach co nhieu hudng thiet ke, co nhieu dang, nhieu loai cau
hoi, bai tap nham hudng hoc sinh (HS) den nhung don vi kien thiic nha't
dinh. He thdng cac cau hoi trac nghiem khach quan d cudi bai nham giup HS
on tap va nang cao ki nang phan doan, quy nap, tijr dd xac dinh duoc noi
dung kidn thiic chu yeu va co ban ciia bai hoc.
Bo sach duoc cac tac gia cd nhieu kinh nghiem trong giang day, trong
nghien cuu khoa hoc (dac biet cd nhieu tac gia da nghien ciiu nhung phSn
mem de hd tro trong giang day, nha't la cac mdn hoc khoa hoc tu nhifen, toan
hoc...). Bien soan bg sach ra ddi hy vong giiip ban doc cd mdt each nhin
mdi, phucmg phap mdi. Cac each thiet ke trong bo sach nay vtta cd tmh dinh
hudng, vita cu the, nham tao ra cac hudng md de giao vien (GV) ap dung ddi
vdi nhiing ddi tugng HS khac nhau.
Tuy da nghien ciiu va bien scan cin than, soiig khdng the tranh nhiing sai
sdt, tac gia kfnh mong dugc su gdp y ciia ban dgc.
TAC GIA



CHlTdNG I
HAM SO Ll/dNG GIAC
•

VA PHlTdNG TRINH LlTdNG GIAC
^

giac khac.
Hieu khai niem cac ham sd lugng giac y =sinx, y = cosx, y = tanx,
y = cot X va tinh chat tuSn hoan cua chung.
Nam dugc su bie'n thien va hinh dang dd thi cua cac ham sd lugng giac
neu tren.
2. KT nang
Sit dung thanh thao cdng thiic nghiem.
Giai thanh thao cac phucmg trinh lugng giac cof ban va mdt sd dang phucmg
trinh lugng giac khac.
Bie't xet su bie'n thien, ve dd thi cua cac ham sd lugng giac y — siiu,
y = cosx, y = tan X, y = cot x va mgt sd ham sd lugng giac dofn gian khac.
Giai thanh thao cac phucmg trinh lugng giac ca ban.
Bie't each giai mgt sd dang phucmg trinh lugng giac khdng qua phiic tap cd
the quy dugc ve phucmg trinh bac nhit va bac hai dd'i vdi mdt ham sd
lucmg giac.
3. Thai do
Tu giac, tich cue, ddc lap va chu ddng phat hien cung nhu linh hdi kie'n
thiic trong qua trinh hoat ddng.
cdn than, chinh xac trong lap luan va tinh toan.
Cam nhan dugc thuc te' cua toan hge, nh^t la ddi vdi lugng giac.
III. CAU TAO C O A C H U O N G

Du kie'n thuc hien trong 17 tiet, phan phdi cu thi nhu sau :

6

§ 1. Cac ham sd lugng giac

(3 tie't)


gdc (cung) lugng giac va mgt sd cdng thiic lugng giac. Lugmg giac ldp 11
la su ndi tie'p chucmg trinh lugmg giac ldp 10. Dac diem dd ddi hdi giao
vien phai luu y nhae lai hay ggi md cho hge sinh nhd lai cac kidn thiic d
ldp 10 cd lien quan den bai hoc de de dang tiep thu kien thiic mdi.
2) O ldp 10 chi ndi den cac gid tri lugng giac ciia gdc hay cung lugng giac a.
Sang ldp 11, khi ndi den cac ham sd lugng giac y =sinx, y = cosx,
y = tan X, y = cotx ta hieu x la sd thuc va la sd do radian cua gdc hay
cung lugng giac.
3) Day la lan dau tien hge sinh lam quen vdi ham sd tuin hoan. Tuin hoan la
tfnh cha^t ndi bat cua cac ham sd lugng giac nen mac dii chuomg trinh
khdng yeu cau trinh bay tdng quat ve ham sd tuin hoan, cac tac gia vSn
gidi thieu dinh nghia ham sd tuin hoan (cudi §1) nham nhdc nhd hge sinh
chii y tfnh chat tuan hoan cua cac ham sd lugng giac.
4) Yeu ciu ve giai cac phucmg trinh lugng giac d day dugc giam nhe ra't nhidu
so vdi trudc day. Dieu dd the hien d hai didm co ban :
- Chi neu cac dang phuomg trinh dom gian, khdng ddi hdi phai cd nhiing
thu thuat bie'n ddi lugng giac phiic tap, va neu cd cac didu kien kem theo
thi viec thir lai cac dieu kien dd kha dem gian.
- Khdng yeu ciu giai va bien luan phucmg trinh lugng giac chiia tham sd.
Tuy nhien, giao vien can chu y ren luyen cho hoc sinh kT nang giai cac
phucmg trinh lugng giac ccr ban that thanh thao. Dd la ccf sd dd hoc sinh nang
cao kT nang giai cac phuomg trinh phiic tap hom.


P h a n 2>
CAC B A I SOAI^

§1. Cac ham so' Itfctog giac
(tiet 1, 2, 3)
I. MUCTIEU

Bai nay chia lam 3 tie't r
Tie't 1 : Tif ddu den hit phdn I.
Tiet 2 : Tiep theo den hit phdn 2.
Tiet 3 : Tiep theo den hit phdn 3 vd bdi tap.
IV. TIEN TRINH DAY HOC
A. DAT VXN"DE

Cdu hoi I
Xet tinh diing - sai cua cac cau sau day :
a) Ndu a > b thi sina > sinb.
b) Ndu a > b thi cosa > cosb.
GV : Ca hai khang dinh tren deu sai. Cd the dan ra cae vf du eu the.
Cdu hoi 2
Nhiing cau sau day, cau nao khdng cd tfnh diing sai?
a) Neu a > b thi tana > tanb.
b) Neu a > b thi cota > cotb.
GV : Ta tha'y : Ca hai cau tren deu diing. Sau day, chiing ta se nghien ciiu ve cac
tfnh chat ciia cae ham sd y = sinx, y = cosx, y = tanx va y = cotx; su bie'n thien
va tfnh tudn hoan eiia eac ham sd dd.


B. BAI M6I
HOAT DONG 1
I, Cac ham sd y = sinx va y = cosx
• Thuc hien |H1| trong 3'
Muc dich.
Nhae lai each xac dinh sin x, cos x de chuydn tidp sang dinh nghTa cac ham
sd sin va cosin.
Hoqt dgng cua GV


.

,COS27t.

4,

sm—= 1,
2
•

•^

1

( n] ^
0
1
cos — = — ,cos27t = l .

I 4j 2

a) Dinh nghia
• GV ggi hai hge sinh nhae lai cac gia tri lugng giac sin va cdsin. Sau dd GV
neu dinh nghia.
Quy tdc dgt tuong img mdi sdthitc x vdi sin cua gdc lugng giac cd sd
do radian bang x dugc ggi la hdm sd sin, ki hieu /ay = sinx .
Quy tdc dgt tucmg Ung mdi sdthuc x vdi cdsin ciia gdc lugng giac cd
sddo radian bdng x dugc ggi la hdm sd cosin, ki hieu Id y = cos x.
10


c) Su bien thien ctia hdm sdy = sinx
• GV dua ra cau hdi

11


?3|

Neu lai chu ki tudn hoan cua ham sd y = sinx. Tfnh tudn hoan cua cae
ham sd dd cd lgi fch gi trong viec xet chidu bi6i thien cua cac ham
sd dd.

?4|

De xet chieu bidn thien eua cac ham sd dd ta can xet trong mdt
khoang cd do dai bao nhieu?

?5|

Hay neu mdt khoang de xet ma em eho la thuan lgi nha't.

• Sir dung cac hinh 1.2, 1.3 de md ta chidu bie'n thien cua ham sd dd trong doan
[-Tt; Tt].

,

B

0
A'\


y = sinx
12

Tt

-Tt

2"

0

1

Tt


• De ve dd thi ham sd GV cdn eho HS tim mdt sd eac gia tri dac biet bang each
cho HS didn va chd trdng sau day :
X

0

y = sinx

...

Tt

Tt

• GV neu nhan xet trong SGK :
1) Khi X thay ddi, ham sd y = sinx nhan mgi gia tri thudc doan [-1; 1]. Ta ndi
tap gid tri ciia ham sd y = sinx la doan [-1; 1].
2) Ham sd y = sinx ddng bidn tren khoang

Tt

Tt

•2'2

Tuf dd, do tfnh chtft

tudn hoan vdi chu ki 2TI, ham sd y = sinx ddng bidn tren mdi khoang
- - + k2Tt; - + k2Tt \,

keZ.

• Thuc hien |H3| trong 3'
Muc dich
, (n 3n^ "
- Nhan bifit tfnh nghich bidn cua ham sd y = sinx tren khoang — ; — nhd
v2 2 /
dd thi (bang bidn thien chi mdi xet tren (-Tt; Tt)); dieu dd cdn giiip ren luyen
ki nang dgc.
- Nhd tfnh chdt tudn hoan vdi qhu ki 2Tt ciia ham sd y = sinx de suy ra ham sd
dd nghich bidn tren cac khoang — + k2Tt;
v2
2
Hoqt dpng cua GV

nd
nghich
bidn
tren
mgi
^Tt , ,,
3Tt , ^ '
—+ k2Tt; — + k2Tt , k e Z .

U

2

khoang —+ k2Tt ; — + k2Tt •)

U

j

2

J

k &Z.

d) Su bien thien cda hdm sdy = cosx
• GV dua ra cau hdi
?10| Neu lai chu ki tudn hoan cua ham sd y = cosx. Tfnh tudn hoan ciia
ham sd dd cd lgi fch gi trong viec xet chieu bien thien cua cac ham sd dd.
?11|


-1


De ve dd thi ham sd GV cdn cho HS tim mdt so cac gia tri dac biet bang each
cho HS dien va chd trdng sau day :
0

Tt

Tt

Tt

Tt

2Tt

3Tt

'e

'4

3^

i

T


Ggi y tra Idi cau hoi 2

Nhan xet ve tfnh tang, giam ciia Khi M chay tren dudng trdn lugng
ham sd y = cosx khi M chay tur giac theo chieu duomg tiir A de'n A',
A ddn A'
diem H chay dgc true cdsin tii A den A'
nen OH tlie la cosx giam tur 1 ddn - 1 .
• GV neu nhan xet trong SGK :
1) Khi X thay ddi, ham sd y = cosx nhan mgi gia tri thudc doan [rl; 1]. Ta ndi
tap gid tri ciia ham sd y = cosx la doan [-1; 1].
2) Do ham sd y = cosx la ham sd chSn nen dd thi ciia ham so y = cosx nhan true
tung lam true ddi xiing.
15


3) Ham sd y = cosx ddng bien tren khoang (-Tt; 0). Tii dd do tfnh chat tudn hoan
vdi chu ki 2Tt, ham sd y = cosx ddng bien tren mdi khoang (-Tt + ^2Tt; ^2Tt),
A:e Z.
Thuc hien |H5| trong 3'.
Muc dich
Xet tfnh ddng bie'n va nghich bie'n eua ham sd y = cosx tren doan [-Tt; Tt].
Hoqt dpng da GV

Hoqt dpng cua HS

Cdu hoi I
Ggi y tra Idi c^u hoi 1
Nhan xet vd tfnh ddng bien va Quan sat dd thi, ta thay ham sd
nghich bidn cua ham so
y = cosx nghich bidn tren khoang

ki...;
ki...;
- Ddng bie'n tren mdi khoang
va nghich
khoang...

bidn

- Ddng bien tren mdi khoang ...
va nghich bie'n tren mdi khoang

tren mdi

- Cd dd thi la mgt dudng hinh - Cd dd thi la mdt dudng hinh sin.
sin.

16


nOATD(DNG2
2. Cac ham sd y = tanx va y = cotx
a) Dinh nghia
• Neu dinh nghia trong SGK.
Quy tdc dgt tuong iing mdi sdx e 3)^ vdi sd'thuc tan x • sinx duoc
cosx
ggi la hdm sdtang, ki hieu la y = tan x.
• GV dua ra eau hdi
?17| Ham sd y = tan x khdng xac dinh tai nhiing didm nao?
.cosx
Quy tdc ddt tuang ifng mdi sdx e 3)2 vdi sd'thuc cotx ='

• GV dua ra kdt luan cudi ciing:
T = Tt la sd duomg nhd nha't thoa man
tan(x + T) = tanx vdi mgi x G 9)j,
va T = Tt cung la sd duomg nhd nhdt thoa man
cot(x + T) = cotx vdi mgi x G 9)2Ta ndi cac ham sd y = tanx va y = cotx la nhiing hdm sdtudn hodn vdi
chu ki Tt.
c) Subien thien vd do thi cua hdm sdy = tanx
• GV dua ra cac cau hdi sau:
Sir dung hinh 1. 10 de md ta chidu bidn thien cua ham sd dd trong khoang
(--•-)
?23| Trong khoang ( —Tt; 0) ham sd y = tanx ddng bidn hay nghich bidn?
Tt .

?24| Trong khoang (0; —) ham sd y = tanx ddng bidn hay nghich bidn?
Tt TT

GV ke't luan : Ham sd y = tanx ddng bidn trong mdi khoang ( — ; —).
• Thue hien |H6| trong 5'
Hoqt dpng cua GV

Hoqt dpng cua HS

Cdu hoi 1
Ggi y tra Idi c^u hdi 1 '
Tai sao cd thd khang dinh ham Ta da bidt, ham sd y = tanx ddng
sd y = tanx ddng bidn tren mdi
bidn tren khoang — ; — nen do
khoang
Tl


Tt

dudng thang vudng gdc vdi true hoanh, di qu^ didm — + kTt; 0 ggi la mdt
2
dudng tiem can ciia dd thi ham sdy = tan x.
d) Subien thien cua hdm sdy = cotx
• GV dua ra cac cau hdi sau dd HS khao sat.
Tt

1

?25| Trong khoang (0; —) ham sd y = cotx ddng bie'n hay nghich bidn?
1

Tt

,

V

?24| Trong khoang (—; Tt) ham so y = cotx ddng bidn hay nghich bidn?
z
GV kdt luan : Ham sd y =; cotx ddng bidn trong mdi khoang (0; TI).
Sau dd GV sit dung hinh 1.12 de md ta dd thi cua ham sd y = cotx.
• Dd ghi nhd GV cho HS dien vao chd trdng sau:
Ham so y = tanx
- Cd tap xac dinh la ...;
- Cd tap gia tri la...;
- L a ham sd...;
- La ham so tudn hoan vdi ehu ki...;

?25| Ham sd y = 2sin x tudn hoan hay khdng? Ndu la ham so tudn hoan
hay chi ra chu ki?
?26| Ham sd y = -32cos x tudn hoan hay khdng? Ndu la ham sd tudn hoan
hay chi ra chu ki?
?27| Ham sd y = 2sin — tudn hoan hay khdng? Ndu la ham sd tudn hoan
hay chi ra ehu ki?
?27| Ham sd y = Stan x tudn hoan hay khdng? Ndu la ham sd tudn hoan
hay chi ra chu ki?
?28| Ham sd y = -3cot x tudn hoan hay khdng? Ndu la ham sd tudn hoan
hay chi ra chu ki?
?29| Ham sd y = 2cot2x tudn hoan hay khdng? Ndu la ham sd tudn hoan
hay chi ra chu ki?
Sau dd GV dua ra cac eau hdi sau nham cung cd bai hge:
Chon diing sai md em cho Id hop ly.
n.
?30| Ham sd y = sinx nghich bien tren khoang (0; —).
(a),Dung;
20

(b) Sai.


1

. 1

'

•>


Tt

?34| Ham so y = cosx nghich bien tren khoang (0; —).
(a) Dung;

(b) Sai.

1

Tt

?35| Ham sd y = cosx nghich bidn tren khoang (—; 0).
(a) Diing;
1

(b) Sai.
V

,

Tt

?36| Ham sd y = cosx ddng bidn tren khoang (0; —).
(a) Diing;
1

(b) Sai.
V

,

Sai.

Tt

?40| Ham sd y = tanx nghich bidn tren khoang (0; —).
(a) Dung;

(b) Sai.
21


HOAT DONG 4

TOM TAT BAI H O C
1. Quy tac dat tucmg iing mdi sd thuc x vdi sd thuc y = sinx. Quy tac nay dugc
ggi la ham sd sin.
sin :

R -> M
X i-> y = sinx.

• y = sinx xac dinh vdi mgi x e R va -1 < sinx < 1.
• y = sinx la ham sd le.
• y = sinx la ham so tudn hoan vdi chu ki 2;r.

°^f

Ham sd y = sinx ddng bidn tren

va nghich bidn tren


• y = tanx xac dinh vdi moi x 9^ — + ICTT, k e Z.
^

22

•

•

2


• y = tanx la ham sd le.
• y = tanx la ham sd tudn hoan vdi chu ki n.
Ham Sd y = tanx ddng bidn tren nura khoang

°1

4. Ham so cdtang la ham sd dugc xac dinh bdi cdng thiic
cosx

..
^.
(sinx -^ 0).

y = cot =

sinx
Tap xac dinh cua ham sdy = cotx la %2 - ^ ^ \kTi | it G Z}


23