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Tgp chi Khoa hgc Trudng Dgi hpc Cdn Tho Phdn C Khoa hpc XS hgi Nhdn vdn vd Gido due 33 (2014) 90 97 Tap chl Khoa hpc TriTdng €)ai hpc Can Thd website sj ctu edu vn TO CHlTC TOAN HOC DOI VOI ©INH SIN M[.]
Tgp chi Khoa hgc Trudng Dgi hpc Cdn Tho Phdn C: Khoa hpc XS hgi Nhdn vdn vd Gido due: 33 (20 Tap chl Khoa hpc TriTdng €)ai hpc Can Thd website: sj.ctu.edu.vn TO CHlTC TOAN HOC DOI VOI ©INH SIN: MOT KHAO SAT THEO CACH TIEP CAN NHAN CHIING HOC TRONG DIDACTIC TOAN Nguydn Phii Loc' va Diep Van Hoang^ ' Khoa Suphgm, Trudng Dgi hgc Cdn Tha ^ Ldp Cao hgc khda 19 - Chuyin ngdnh Ly lugn vd Phucmg phdp dgy hgc bg mdn Todn, Khoa Suphgm Thong tin chung: Ngdy nhgn: 03/05/2014 Ngdy chdp nhgn: 29/08/2014 Title: Mathematical organizations of sine theorem: An investigation based on an anthropological approach into mathematical didactics Tu khda: Dfnh ly sin, dgy hgc djnh ly, to chiec todn hgc, didactic todn, tiip can nhdn chiing Didactic todn Keywords: Sine theorem, theorem teaching, mathematical organization, mathematical didactics, anthropological approach into mathematical didactics ABSTRACT Sine theorem in the triangle is an important theorem in geometry curriculum in secondary schools Content of this theorem indicates the relationship between the angles, edges and circumscribed circle's radius in a Piangle Thus, in applications to sine theorem for problem solving, it is possible to change a problem on the relationship among the sides of the triangle to the problem on the relationship among the angles and vice versa In addition, the sine theorem has many practical applications; it is an opportunity that teachers can take advantage of to educate "realistic mathematics" for their students Sine theorem has many meanings as stated, what are mathematical organizations of the theorem in current textbooks? While solving the problems, have stiuients used this theorem as a strategy? This paper will report the results of investigations of into textbooks and students in Phan Ngoc Hien secondary school, Bac Lieu province Dinh ly sin tam gidc la mgt nhdng dinh ly quan trgng chuang trinh Hinh hgc a trudng trung hgc phd thdng Ngi dung dinh ly ndy^ biiu thi mdi quan hi giiia cdc gdc, cgnh vd ban kinh vdng tidn ngogi tiip ciia tam gidc Nhd vdy, img dyng di gidi todn, dinh ly sin cho phep chuyin ddi bdi todn vi mdi liin hi giiia cdc cgnh cita tam gidc sang bdi todn biiu thi mdi lien he giiia cdc gdc vd ngugc lgi Ngodi ra, dinh ly sin cd nhiiu ung dyng thuc liin; ddy la ca hdi md gido vien cd the tdn dung di gido dye tinh thuc tiin cua todn hgc cho hgc sinh Dinh ly sin cd nhieu y nghta nhu da neu, thi thi cdc "td chirc todn hgc " dinh ly sin sdch gido khoa hiin hdnh sao? Trong gidi todn vi tam gidc, hgc sinh co khuynh hudng chgn dinh ly sin nhu Id mgt chiin luge gidi hay khdng? Bdi bdo se tudng thudt kit qud khdo sdt sdch gido khoa vd khdo sdt hgc sinh d Trudng trung hgc phd thdng Phan Nggc Hien, tinh Bgc Lieu CO S d L Y THUYET Ll Tidp cdn nhSn chdng hi^c Didactic to^n Tiep cdn nhan chiing hpc ttong Didactic toan tdp trung nghidn cftu mdi quan he gifta tti thftc va thd che Theo each tidp can nay, mdt ddi tugng toan hpc dugc xem nhu mOt sinh vdt sdi^; v^y, nd cung trdi qua cac giai doan: phat sinh, tdn tgi, phdt ttidn, mat di MOt doi tugng todn hpc khdng thd "sdng" ddc lap, md nd ludn cd nhieu mdi quan he vdi cdc ddi tugng khdc vd gan lien vdi thd chd Phdn C: Khoa hpc Xd hdi Nhdn vdn vd Gido dtfc: 33 (2014): 90-97 Tgp chi Khoa hge Trudng Dgi tigc Cdn Tha ma ddi tugng ndm ttong Y ChevaUard (1992) da vidt: "MOt tri tiiftc khdng tdn tgi ttong xd hOi "rong", mgi tri thftc ddu xudt hidn d mot thdi didm xdc dinh, mdt thd chd va dugc edm sau vao mOt nhidu thd chd" (ddn theo (Trdn Anh Dung, 2013)) Do cdch nhin nhdn vd tri thftc nhu ttdn ndn cdch tidp can nhan chftng hpc ttong Didactic todn nghien cftu xoay quanh hai khdi nidm "tri thftc" vd "thd chd", vd nd dugc cu thd hda thdnh ba ngi dung nghien cuu chinh la: Ly thuydt vd chuydn ddi didactic (Nguydn Phu Lpc, 2008), ly tiiuydt vd quan hd thd chd vd quan hp cd nhdn (Bessot vd ctv, 2010), vd td chftc todn hpc (Bessot vd ctv., 2010; TrdnAnh Dung, 2013)) Trong khudn khd bdi bdo nay, chftng tdi chi de cap vd dp dyng eac lugn didm vd td chftc todn hpc ttong Didactic todn 1.2 To chirc toan hpc Tft quan didm xem hoat dOng toan hoc nhu mOt hogt dpng cua ngudi: chft thd thyc hidn mOt Bl Kieu nhiem vu (neu dang toan can xem xet) V kidu nhidm vu ndo dd frong mdt tiid chd xdc dmh, Y Chevallard (1999), tiieo (Bessot va ctv., 2010), lap ludn rdng tien hanh mOt nhidm vu toan hpc, chu thd phai biet "each thftc" thyc hidn (know how, hay praxis) vd dua rtiiirng ly gidi cho qud trinh hdnh ddng tten ca sd ly thuydt todn hpc lidn quan (knowledge, hay logos); vd tft dd dng da dua khdi niem "td chftc todn hpc" (tidng Anb: praxeology hoac organization; tidng Ph^: praxeologie) gdm bdn thdnh phdn: kidu nhidm vy T, ky thudt T, cdng nghd 0, ly thuydt va dupe md hinh hda nhu sau: [r,t,d,&] (1) Md hinh ed y nghia Id: mdi boat dOng ciia ngudi ddu nhdm thyc hidn nhidm vy t tiiupc kidu nhidm vu T nao nd nhd sft dung ky thudt T, T dugc gidi thich bdi cdng nghd vd cudi cung cdng nghd d duge hpp tiiuc hda bdi IJ thuydt Nhu vdy, md hinh (1) cd the didn gidi Igi nhu sau (xem Hinh 1) B2 Ky thuat (trinh bay each giai cho dang toan neu a Bl) B3 Cong nghe (neu cac tri thuc Iam ca scr; ly giai cho ky thuat giai a B2) B4 Ly thuyet (hop thiic hoa trithucab.3; chi ro ly thuydt lam CO sor cho tri thuc d B3) _y V_ y Cdch thuc thicc hien nhiem VM (hoac qiiy trinh hdnh ddng di hodn thdnh nhiem vu) Tri thiic vd ly thityet duac dung ly gidi cho cdch thuc thuc hien nhiem vw Hinh I: Sof dd dien giai "td chirc toan hpc" (praxeology) frong Didactic toan theo cdch tidp c$n nhdn chung hpc PHAT BIEU VAN DE NGHIEN CUtJ Dinh ly sin ttong tam giac (Hinh hpc 10), mdt dinh IJ "da ddng thftc", nd bidu thj mdi quan h? gifta ba cgnh vdi ba gdc vd ca ban kinh vdng ttdn ngo^ tidp efta mdt tam g i ^ Cftng vdi djnh ly eosin, dinh ly sm ludn cd mat ttong cac sach giao khoa ve Hinh hpc qua cdc th6i ky khac eua vide thay ddi sdch Do dinh ly sin cd vi tti quan ttpng ttong chuong trinh HInh hpc nhu vdy, vd hidn vdi cdch tidp can nhdn chung hpc Didactic toan cho phep chftng ta thyc hi^n nhftng khao cim vd td chftc toan hpc xoay quanh mdt doi tugng toan hgc mOt cdch sdu sdc Dd gdp phdn hidu bidt ve thyc tien vd nOi dung chuong ttinh lidn quan ddn dinh Iy sin, chung tdi khdo sdt dinh ly sin vdi hai cdu hdi nghidn ctiu sau ddy: Cdu hoi thu nhdt: Theo cdch tidp can nhdn chftng hpc ttong Didactic toan, td chftc toan hpc ddi vdi djnh Iy sin ttong ttong hai bd sdch giao khoaHinhhpc lOvdHmhhpc 10 ndng cao sao? Tgp chi Khoa hge Trucmg Dgi hgc Cdn Tha Phan C: Khoa hge Xd hgi Nhdn vdn vd Gido due: 33 (2014): 90-97 Cdu hdi thu hai: Sau hpc djnh Iy sin mdt thai gian dai, giai tam gidc cd nhidu hpc sinh dp dung dinh ly sin dd gidi hay khdng? Va thyc td vide sft dyng djnh ly sin ttong ttinh bdy ldi gidi todn cua cdc em hpc smh sao? PHU'CfNG PHAP NGHIEN CUtJ VA D6I TU*ONG KHAO SAT - Phan tich npi dung (Nguydn Phu LOc, 2014); Phan ti'ch nOi dung todn hgc lidn quan ddn dinh IJ sin ttong Chung tdi phdn tieh cdc sdch sau ddy: Mi; Ei; Gi ldn lugt la Hinh hoc 10 - ndng cao (Vdn Nhu Cuong va ctv., 2006a), Bai tap Hinh hpc 10 - nang cao (Vdn Nhu Cuang vd ctv., 2006b), Hinh hpc 10 nang cao -Sach giao vidn (Vdn Nhu Cuong va ctv., 2006c) Mi; E2; G2 ldn lugt la Hinb hpc 10 (Trdn Van Hao vd ctv., 2006a), Bdi tdp Hinh hpc 10 (Trdn Vdn Hao vd ctv., 2006b), Hinh hgc 10 - Sdch giao vidn (Trdn Vdn Hgo vd ctv., 2006c) ~ Thd nghi$m su ph^m: Xay dyng mdt tmh hudng thft nghidm Id mpt bai todn gidi tam gidc vdi nhidu dft kidn cho phdp gidi bdng mdt sd cdch khdc nliau, ttong dd cd cdch dp dyng dinli IJ sin nhdm kidm nghipm xem hgc sinh uu tidn ehpn each van dyng dinh IJ sin vdo gidi todn, hay khdng vd tiiuc tidn ap dung dinh IJ sin Idi gidi Vdi myc dich kidm nghidm ndu trdn, bdi todn dugc dua thft nghiem se cd cdc bidn tinh hudng sau day: VI: Cho cdc ydu td xdc djnli mOt tam gidc Tinh cdc ydu td cdn lai VI nhgn ba gid tri: VI.1: Bidt hai canh vd-mpt-gdcikep-gijia.— Tinh canh thft ba VI.2: Bidt hai gdc, mOt cgnh kep gifta ho|c bdn kinh vdng trdn ngogi tidp Tinh hai canh cdn lai V1.3: Bidt ba canh Tinh cac gdc V2: Cho bidt didn tich eua tam gidc Tinh mdt canh hoac mOt gdc eua tam gidc V2 nhdn ba gid tri: V2.1 Bidt dipn tich, mpt gdc va mOt cgnh kd Tinh cgnh kd cdn lai V2.2 Bidt di?n tich, hai cgnh Tinh gdc kep gifta V2.3 Bidt dien tfch, hai canh vd bdn kinh vdng ngogi tiep Tinh cgnh cdn lai Tu phdn tich ndu tten ve VI, V2 vd V3, ttong tinh hudng thu nghidm ma chung tdi dua se cd hai bidn VI, V2 , vd cdc gia tti dugc chgn Id: VI.1 vd V1.2 va V2.1 V2.3 Cutiidnhu sau: "Cho tam gidc ABC, bidt AB= c=3, AC=b=2, - ^/^ ^ = 60 , smB = , ban kinh dudng ttdn ngoai tiep R ^121 Syji va dien ti'ch S • Tinh dO dai canh BC (= a)?" (Thdi gian ldm bai 10 phut) Can cu vao the chd vd cdc td chftc toan hpc ddi vdi dinh ly sin, chiing tdi tidn dodn bdi toan ttdn cd the dugc hgc sinh giai bang eac chidn luge sau day: Chiin luac SI (VI, V1.2): Sft dyng dinh IJ sin: - ^ = 2R sin^ Theo dinh li sin ta cd: , , V2T, = 2R.sin A = 2.^^^^.sin 60" = -Jl sin A CUen luge S2 (VI, VI.2)- S i dyng dinli ly sin; a b sin A sin a b — smA S.sinA 2.sin60° sin5 v2I —.' W sin5 ^ = - - = x/7 Chidn luge S3 (VI, Vl.l): Sft dyng djnh li cosin Theo dinh li cosin a^ =b^ -\-c^ - 2bc cos A ta cd: = ^ + ^ - 0 60" = ^a = ^ Chiin lugrc S4 (V2, V2.1, V2.3): Sft dyng cdng thftc didn tich tam giac Theo cdng thuc tinh didn tich tam gidc, ta cd: S -—6csmA Phdn C: Khoa hgc Xd hpi Nhdn van vd Gido due: 33 (2014): 90-97 Tap chi Khoa hoc Trudng Dgi hoc Can The Budc I: Tinh gdc cdn lai (ndu cgnh cdn tinh va cgnh dd bidt ldn lugt Id canh ddi eiia hai gdc thi bo qua budc 1) Hoac ^/21 3^/3 = abc 4R.S 4.- = v/7 => a = 4R be Nhan dinh ban dau: Chidn luge SI, S2 vd S3 cd tiie dugc nhidu hpc sinh ehpn lya vi dp dung UTTC tidp dinh IJ sin va cosin Chidn luge S4 sd ed it hpc sinh lua ehpn vi phdi su dyng cdng thftc tinh didn tich tam giac abc 4i? S=—be sm A (3) hoac S = (4) Hai cdng thftc (3) vd (4) khdng tidn dyng cho bdi toan ndu ttdn - Phdng van gido viin (hinh thdc ddm dqo): Phdng vdn ndm gido vidn cua trudng THPT Phan Ngpc Hidn vd tiiyc td gidng day dinh IJ sin - Boi tuang hgc sink dugtc khao sat: Hpc sinli hai ldp flCI (N=38) vd 12Ci (N=36) thuOc Trudng trung hpc phd thdng Phan Ngpc Hidn, tinh Bgc Lieu Chiing tdi ehpn hpc sinh ldp 11 vd 12 vi cdc em ndy da hpc xong dinh IJ sin trudc dd it nhdt mOt nam Khao sat xem sau hpc dinh Iy mdt thdi gian ddi, ttong gidi tam gidc cdc em thudng ehpn lya cdng thftc ndo, cd van dung dinh IJ sin dt gidi hay khdng? KET QUA VA BAN LU^N 4.1 Td chftc todn hpc doi vdi dinh IJ sin 4.1.1 Kit qud Qua phdn tich cac sach Mi; Ei; M2; E2, chung tdi thu dugc kdt qud Id ed sau kidu nhidm vu xoay quanh dinh IJ sin, cy the Id: Tl: Tim dO dai canh efta tam gidc T2: Tim sd gdc cua tam giac T3: Tim bdn kinh dudng ttdn ngogi tidp cua tam gidc T4: Gidi tam gidc T5: Chiing minh ddng thftc Te: LTng dyngtiiyctd Kiiu nhidm vy Ti: Tim dO ddi canh bidt trudc mdt cgnh vd hai gdc Ky thugt T^: Ky thugt gidi quydt kidu nhi$m vu gdm cdc budc sau: Budc 2: a sin A = b sin S ^ a= 6.sinA sin B (gia sir cdn tim cgnh a) Cong nghe Or Sft dung dinh IJ sin Ly thiQ>it &}• He thftc lugng ttong tam gidc Vidu (7];r|):Xemvidu5,M2,ttang61 Kidu nhidm vu Ti: Tim sd gdc cua tam gidc bidt hai canh vd mOt gdc KJ thudt giai quydt Tj : Budc 1: Tim cgnh cdn lgi ddi didn vdi gdc dd eho (ndu tdn tfu mOt cap cgnh - gdc ddi didn till bd qua budc 1) a Budc 2: _ sin A (gid sft cdn tun gdc B) b _ sinB > sin = sin A Budc 3: Suy gid tti gdc B Cong nghe Qf Sft dyng dinh ly sin Ly thuyit &r He tiiuc lugi^ ttong tam gidc Vi du vd (r2;r2) '• Xem bdi t§p 3, M| ttang 59 Kilu nhidm T3: Tim ban kinh dudng tton ngoai tidp cua tam giac K? tiiudt 73: Budc 1: Fim mgt cap gdc vd canh ddi dipn va = csinA Cdng nghi O^c: Sft dung dinh IJ sin va tdng ba gdc ttong efta mdt tam giac bdng 180° sinC Ly thuyet ©4c: He thuc lupng ttong tam giac Vi du (2^;r^): Xem bai tap 34c, M2,ttang66 Budc 3: Tinh cgnh b: b c sin B sin C Budc3: TinhA=I80"-(B+C): =>b = csinS sinC Kidu nhi^m vu T5: Chung minh ddng tiiftc ttong tam gidc Kytiiudtgiai T^ : Theo tiiu ty cdc budc sau: Cdng nghi 04a: Sft dung dinh Iy sin vd tdng ba gdc ttong cua mdt tam giac bdng 180" Ly thuyit 04a: He thftc lugng ttong tam gidc Vi du(2^;r4^): Xem bai tdp 33a, M2,ttang66 Kidu nhiem vy T4b: Gidi tam gidc bidt gdc A, gdc C vd cgnh c Budc 1: Tinh gdc B= 180" - (A+C) Budc 2: Tinh canh a: sin A _ - ¥) Bidn ddi vd trdi thdnh ve phdi (hodc nguac Chftng minh "Vd trai - Vd phai = 0" _ _ Chiing minh vd phdi vd ve trdi ciing bdng C Budc 2: LTi^ dung dinh li sin vd kidn thftc lidn quan dd bidn ddi suy dieu phdi chftng minh Ky thugt T^l^: a Budc 1: Xac dinh hudng (chidn luge) chiing minh: c _ csinA sin C sin C Budc 3: TInli canh b: Cdng nghi O5: Sft dyng dinh IJ sin vd cdc cdch gidi mdt ddng thftc Ly thuyet 0^: Hd thftc lugng tam gidc, cdc tinh chat dang thuc vd quy tdc dien djch Vi dy (T^;TA '• Xem vi du 4, M2, trang Kidu nhidm vu Te: Gidi bdi toan thyc td b e sin B sin C cs'mB sinC Cdng nghi 04b: Sft dung dinh IJ sin vd tdng ba gdc cua mdt tam gidc bdng 180" Ly thuyit 04i,: He thuc lugng ttong tam gidc Vl dy (^;r^j): Xem bdi tap 33c, M2, trang 66 Kidu nhiem vu Tjc: Giai tam giac bidt gdc C, cgnh a vd b Kytiiugtgiai T^ : Theo thft ty cdc budc sau: Budc 1: Chuydn bdi todn thyc td vd bai todn gidi tam gidc Budc 2:Tun each gidi bai toanxtam^giac- phdt_ bidu ttong Budc I -,-v—w- ™r,, Cdng nghe 06: Dinh li sin vd cdc ky thugt ndu tten Ly thuyit 0c: He thuc lugng ttong tam gidc Vi du (r^; r^): Vi du 3, M2, trang 56: Ky thugt T, : Theo thft ty cdc budc sau: Budc 1: Tinh cgnh theo djnh li cosin: r^ =a^+b^-2ab.cosC Budc 2: Tinh gdc B: b c sin sinC „ 6sinC c Tit vi tri AvdB cua mdt tda nhd, ngudi ta quan sdt dinh C cua mdt nggn niii Biit rdng dg cao AB Id 70 m, phuong nhin AC tgo vdi phuang ndm ngang gdc 30", phucmg nhin BC tgo vdi phuang nam ngang goe 15°30' Hoi nggn nui cao bao nhiiu met so vai mat ddt? Phdn C: Khoa hge Xd hgi, Nhdn vdn vd Giao dux:: 33 (2014): 90-97 Tgp ehi Khoa hge Trudng Dgi hge Cdn Tha c Thong ki kiiu nhiim vu Trong Bdng dudi day, chung tdi thdng kd sd bai tgp thupc mdi td chftc todn hpc dd dugc chi rd d ttdn Bang tiidng kd ndy bao gdm 136 bdi toan dugc phan 06 kieu nhidm vy cau hdi, do: Cd 20 cdu Id nhiing vi dy vd boat dOog co mat ttong phdn IJ thuydt efta M j , M2 Cd 116 cdu dugc d e nghj ttong phdn bai iSp ciia M l , M2 vd El, £2- Bang 1: T h d u g kd theo bai t d p theo kidu nhidm vu Vidu - Hoat dong Bai tap Bai tap Bai t a p Bai t a p Tong so Trong Ml !Vl! troDg El t r o n g E l bai tSp K i l u nhi£m vu Ky thuat T, Tim dai canh cua tam gidc n 2"2 2 18 T 24 h 10 28 ^5 ^6 3 13 20 16 29 33 38 13< •'•2 Tim so goe ciia tam gidc Ts Tim ban kinh duong tron ngoai tiep tam fiiac T Giai tam gidc Tj Chijmg minh ddng thijc tam gidc T6 LTng dung th\TC te TSne cans 4.1.2 24 Bdn lugn Td chftc todn hpc ddi vdi djnh IJ sin ttong hai sach dugc khdo sdt nhin chung Id tuang ddng Hai sdch deu dua kidu nhidm vu (dang todn) eho dinh ly sin Cd hai sdch ddu cd quan tdm dua cdc bai toan npi dung thyc td dd eho thdy khd nang ftng dung efta dinh ly sin Nhin chung, cac tdc gid sach gido khoa qudn ttidt tinh thdn ddi mdi giao dye Cdc kieu nhidm vu d muc dO van dung cdp tiiap, khdng "sa ldy" vdo cdc dgng bai t§p phuc tap vd qud khd 4.2 Kdt q u a k h a o sdt viec v a n d u n g dinh li sin ciia hpc sinh 4.2.1 Kit qud khdo sdt Kdt qud lam bai eua h p c sinh ddi vdi bdi todn md chung tdi dua t h u nghiem hpc sinh (dk bai d muc 3) d u g c tdng kdt n h u sau (xem Bang 2): Tgp chi Khoa hgc Trudng Dgi hgc Cdn Tha Phdn C Khoa hge Xa hgi Nhdn w a Gido due- 33 (2014): 90-97 ^^Pg 2: Bang thdng ke ve chien luge giai Ldp SI sd Dinh Ii sin sin A Dinh li cosin Cdng thirc didn tich tam giac sin B y5m.A ) (0,0%) I2CI 36 4(11,11%) (5,55%) 30 (83,33%) (0,0%) tiet hay thi hpc Id thudng bgn che cho bdi tap ed 4.2.2 Bdn ludn lidn quan ddn dinh li sin (theo J kidn cua thdy Dya vao kdt qua thu dugc (Bang 2) vd vide xem T.T.H), vay dinh li sin dang bi xem nhe vd ting xet bdi ldm efta bpc sinh, chftng tdi cd mOt sd y dung ciia nd dang bi "thu hep" ddn kien ban ludn sau ddy Ket qud khdo sat va vdi cac J kien efta gido - Tdt cd hoc sinh (74 em) ddu lam bdi: 58 hpc vidn, dinh IJ sin khdng phdi la nOi dung ttpng tdm sinh ehpn chidn luge dinh Ii cosin nhimg ttong tinh cua chuang ttinh toan hpc phd thdng Gido vien todn cd ddn 44 HS gidi sai ho^ie chua hoan tiiidn khdng danh nhidu thdi gian luydn tap cho hpc sinh Trong dd, chl cd 16 hpc sinh ehpn chidn luge Tuy vay, ttong thyc td khao sdt vdn cd 16/74 (21, dinh li sin: 11 em sft dyng ddng thftc: 62%) em sft dung dinh IJ sin vao gidi todn va tdt cd deu ttinh bdy Idi giai chinh xdc Didu ndy ndi ldn = 2R djnh Ii sin dd gidi bdi toan vd 05 rang dinh ly sin khdng phdi la ndi dung khd nhd vd sin A kho van dung so vdi dinh Iy cosin hpc sinh cdn lai thi chgn ddng thftc: a b KET LUAN = ; cd 16 Idi gidi dung vd cho kdt qua sin A sin B Qua ket qua nghien cftu thu dugc ddi vdi dinh IJ sin - mdt ddi tugng toan hpc- nhu da tudng thudt chinh xde tten day, cho phep chftng ta kdt ludn rdng vide khdo - Hpc sinh cd Idiuynh hudng su dung dinh ly sat cac td chuc toan hoc doi vdi mdt ddi tugng todn cosin de gidi tam gidc han Id dp dyng dinh IJ sin: hpc ttong mOt thd chd xdc djnh theo hudng tiep cdn 73% d Idp ICi vd 83% d Idp 12C, nhan chiing hpc ttong Didactic todn sd cho giao vidn toan thay mgt cdch toan didn cae kieu nhidm De IJ gidi thyc tidn neu tren, chiing tdi da ttao vy tuong ling vdi ddi tugng todn hpc dd Vd sy van doi vdi mdt so giao vien eua trudng ndy dd timg dung dinh Iy sin, dft cd it hpc sinh uu tien vdn dyng dgy ldp 10, vd J kidn eua cac tiidy vd cd nhu sau: dinh ly sin ttong gidi todn nhung nhiing em vdn - Khi ldn ldp, chl ddnh khoang 15 phut eho dyng dinh IJ sin vdo gidi todn ddu cho ldi gidi gidng gidi nOi dung djnh Ii sin (theo J kidn cda thdy dftng Do vdy, gido vidn cdn cd cdc chien luge day L.T.LvdcdV.T.X.M) hpc cho hgc sinh quan tam hon vide van dyng - Dinh li sin ngdn gpn; ndn vide tiep can dinh IJ vao gidi toan tam gidc d^ gdp phdn ndng hai klid, trim tugng (theo J kien cua thdy N.N.P), cao chdt lugng vide day hgc todn efta minh vi vdy chi ydu cdu hpc sinh thira nhdn dinh Ii vd TAI LIEU THAM KHAO bidt cdch dp dung, khdng cdn chiing minh (vi nd rudm ra) I Bessot, A., Comiti, C , Le Thi Hoai Chdu, Dinh Ii sin khdng duge su dyng rtiiidu ttong Ld Van Tien, 2010 Nhftng ydu td ca ban ciia Didactic toan NXB Dai hpc qudc gia chuang ttinh Todn 10 va cdc ldp kd tidp (theo J TP Hd Chi Minh kidn cua ed P.A.T.H) Vi the gidng dgy, nd it dugc quan tdm, mang tinh ddi phd eho du chuang ^ Van Nhu Cuong & cfv, 2006a Hinh hpc trinh 10 ndng cao NXB Gido due Ha NOi - Nhittig djnh Ii mang ti'nh chdt "da ddng VanNhuCuang&cft', 2006b Bdi tdp hinh thftc" nhu djnh li sin thi HS thudng gap khd khdn hpc 10 nang eao NXB Gido due Hd Npi ttong van dyng gidi bdi tgp, vi thd ttong kidm tra 1 (2,63%) (23,68%) 28 (73,68%) Tgp chi Khoa hgc Trudng Dgi hgc Can Tha Van Nhu Cuong & c/v, 2006c Hinh hpc 10 ndng cao - Sach gido vidn NXB Giao due Ha NOi Trdn Anh Dung, 2013 Day hpc khai nidm ham sd Udn tuc d trudng trung hpc phd thdng Ludn dn tidn sT, Tnrdng Dai hpc su phgm TP Hd Chi Minh Trdn van Hao &C/V, 2006a-Hinh hpc 10 NXB Gido due HaNoi Phdn C: Khoa hgc Xo hgi, Nhdn -van vd Gido due: 33 (2014): 90-97 Trdn VdnHao&c/v, 2006b Bdi tap Hinh hgc 10 NXB Giao dye Hd Ndi Trdn Vdn Hao &C/V, 2006c Hmh hpc 10Sdch gido vien NXB Gido dye Ha NOi9 Nguydn Phu Lpc, 2008 Gido trinh joi hudng dsQ' hoc khdng truydn tiidng.Trudng Dai hpc can Tha 10 Nguydn Phft Lpc, 2014 Phuong phap nghien cftu ttong Giao due NXB Dai hpc can Tha ... li sin ta cd: , , V2T, = 2R .sin A = 2.^^^^ .sin 60" = -Jl sin A CUen luge S2 (VI, VI.2)- S i dyng dinli ly sin; a b sin A sin a b — smA S.sinA 2 .sin6 0° sin5 v2I —.'' W sin5 ^ = - - = x/7 Chidn luge... vdi dinh ly sin, chiing tdi tidn dodn bdi toan ttdn cd the dugc hgc sinh giai bang eac chidn luge sau day: Chiin luac SI (VI, V1.2): Sft dyng dinh IJ sin: - ^ = 2R sin^ Theo dinh li sin ta cd:... c sin B sin C Budc3: TinhA=I80"-(B+C): =>b = csinS sinC Kidu nhi^m vu T5: Chung minh ddng tiiftc ttong tam gidc Kytiiudtgiai T^ : Theo tiiu ty cdc budc sau: Cdng nghi 04a: Sft dung dinh Iy sin