Luonggiac-Chuong3 - LNG GIC C HNG III PHNG TRNH BA C HAI V...

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L ƯỢ NG GIÁC CHÖÔNG III: PHÖÔNG TRÌNH BAÄC HAI VÔÙI CAÙC HAØM SOÁ LÖÔÏNG GIAÙC ( ) () ++ = = += = = 2 2 2 2 asin u bsinu c 0 a 0 acos u bcosu c 0 a 0 atg u btgu c 0 a 0 a cot g u b cot gu c 0 a 0 Caùch giaûi: Ñaët : hay vôùi ts i n u = tc o s u = t1 (ñieàu kieän tt g u = uk 2 π ) o t g u = π Caùc phöông trình treân thaønh: 2 at bt c 0 + Giaûi phöông trình tìm ñöôïc t, so vôùi ñieàu kieän ñeå nhaän nghieäm t. Töø ñoù giaûi phöông trình löôïng giaùc cô baûn tìm ñöôïc u. Baøi 56: (Ñeà thi tuyeån sinh Ñaïi hoïc khoái A, naêm 2002) Tìm caùc nghieäm treân ( cuûa phöông trình ) 0, 2 π cos3x sin 3x 5s inx 3 c o s2 x* 12 s i n 2 x + ⎛⎞ + ⎜⎟ + ⎝⎠ Ñieàu kieän: 1 sin 2x 2 ≠− Ta coù: ( ) ( ) 33 sin 3x cos 3x 3sin x 4 sin x 4 cos x 3cos x + ( ) 22 3co sx s 4co s x s in x cos x sin x 3 4 cos x cos x sin x sin x cos x sin x 1 2sin 2x =− + ⎡⎤ + + + ⎣⎦ + Luùc ñoù: (*) ( ) ( ) 2 5 sin x cos x sin x 3 2cos x 1 ⇔+ = + 1 do sin 2x 2 2 5cosx 2 0 ⇔− + =
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() 1 cos x 2 cos x 2 loaïi = = x 3 π ⇔= ±+ π k 2 (nhaän do 31 sin 2x 22 = ±≠ ) Do ( ) x0 , 2 ∈π neân 5 xx 33 π π =∨= Baøi 57: (Ñeà thi tuyeån sinh Ñaïi hoïc khoái A, naêm 2005) Giaûi phöông trình: ( ) cos 3x.cos2x cos x 0 * −= Ta coù: (*) 1c o s 6 x o s 2 x .cos2x 0 ++ cos6x.cos2x 1 0 ⇔− = (**) Caùch 1 : (**) 3 4 cos 2x 3cos2x cos2x 1 0 = = 42 4 cos 2x 3cos 2x 1 0 ⇔−− 2 2 cos 2x 1 1 cos 2x voâ nghieäm 4 = =− sin 2x 0 k 2x k x k Z 2 π π = Caùch 2 1 cos8x cos4x 1 0 2 ⇔+ = 2 cos 8x cos 4x 2 0 2cos 4x 3 0 1 3 loaïi 2 ⇔+− = = = k 4x k2 x k Z 2 π π = Caùch 3: phöông trình löôïng giaùc khoâng maãu möïc: cos6x cos2x 1 1 == Caùch 4: +− = cos 8x cos 4x 2 0 cos 8x cos 4x 2 = cos 8x cos 4x 1 = cos 4x 1 Baøi 58: (Ñeà thi tuyeån sinh Ñaïi hoïc khoái D, naêm 2005) 44 3 cos x sin x cos x sin 3x 0 ππ ⎛⎞ ++− ⎜⎟ ⎝⎠ 2 =
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Ta coù: (*) () 2 22 2 2 13 sin x cos x 2sin x cos x sin 4x sin 2x 0 ⎡⎤ π ⎛⎞ ⇔+ + +− ⎜⎟ ⎢⎥ ⎝⎠ ⎣⎦ 2 = [] 2 11 3 1 sin 2x cos 4x sin 2x 0 2 ⇔− + − + − = 1 1 sin 2x 1 2sin 2x sin 2x 0 2 2 + = 2 sin 2x sin 2x 2 0 = sin 2x 1 sin 2x 2 loaïi = =− π ⇔= + π π ⇔=+π∈ ± ± 2x k2 , k 2 xk , k 4 Baøi 59: (Ñeà th ïc khoái B, naêm 2004) i tuyeån sinh Ñaïi ho ( )( −= 2 5sinx 2 3 1 sinx tg x * ) Giaûi phöông trình: Khi ñoù: (*) cos x 0 sin x 1 ≠⇔ ± Ñieàu kieän: 2 2 sin x 2 sinx cos x = 2 2 sin x 2 1s i nx = 2 3sin x 2 i n x = + 2 2sin x 3sinx 2 0 = 1 sin x nhaän dosin x 1 2 sin x 2 voâ nghieäm =≠ ± 5 2 x k 2 k 66 ππ ⇔=+ π ∨= + π∈ Z 2sin 3x 2cos3x * sin x cos x + Baøi 60 : Giaûi phöông trình: Luùc ñoù: (*) sin 2x 0 2s in3x cos3x sin x cos x = +
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() ( ) 33 11 2 3 sin x cos x 4 sin x cos x sin x cos x ⎡⎤ ⇔+ + = + ⎣⎦ ( ) 22 sin x cos x 2 sin x cos x 3 4 sin x sin x cos x cos x sin x cos x + + = 1 sinx cosx 2 8sinxcosx 0 sin x cos x + = ⎢⎥ 2 sin x cos x 4 sin 2x 2 0 sin 2x = 2
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This note was uploaded on 11/26/2011 for the course MATH 1002 taught by Professor Chuck during the Spring '11 term at University of Western States.

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Luonggiac-Chuong3 - LNG GIC C HNG III PHNG TRNH BA C HAI V...

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