Luonggiac-Chuong1 - CHNG 1: CONG THC LNG GIAC I. nh ngha...

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CHÖÔNG 1: COÂNG THÖÙC LÖÔÏNG GIAÙC I. Ñònh nghóa Treân maët phaúng Oxy cho ñöôøng troøn löôïng giaùc taâm O baùn kính R=1 vaø ñieåm M treân ñöôøng troøn löôïng giaùc maø sñ ± AM = β vôùi 02 ≤β≤ π Ñaët k2 ,k Z α=β+ π ∈ Ta ñònh nghóa: sin OK α= cos OH sin tg cos α α vôùi co s 0 α≠ cos cot g sin α α vôùi sin 0 II. Baûng giaù trò löôïng giaùc cuûa moät soá cung (hay goùc) ñaëc bieät Goùc α Giaù trò () o 00 o 30 6 π o 45 4 π o 60 3 π o 90 2 π sin α 0 1 2 2 2 3 2 1 cos α 1 3 2 2 2 1 2 0 tg α 0 3 3 1 3 || cot g α || 1 3 3 0 III. Heä thöùc cô baûn 22 sin cos 1 α+ 2 2 1 1t g cos = α vôùi kkZ 2 π α≠ + π 2 2 1 tc o t g sin += α vôùi ( ) α≠ π IV. Cung lieân keát (Caùch nhôù: cos ñoái, sin buø, tang sai π ; phuï cheùo) a. Ñoái nhau: vaø −α α ( ) sin sin −α = − α ( ) cos cos −α = α ( ) ( ) tg tg −α = − α ( ) ( ) cot g cot g −α = − α
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b. Buø nhau: vaø α π−α ( ) () sin sin cos cos tg tg cot g cot g π−α = α π−α =− α π−α =− α α c. Sai nhau : vaø π+ π α α ( ) sin sin cos cos tg t g cot g cot g π+α =− α α π+α = α α d. Phuï nhau: vaø α 2 π −α sin cos 2 cos sin 2 tg cot g 2 cot g tg 2 π ⎛⎞ −α = α ⎜⎟ ⎝⎠ π α π α π −α = α e.Sai nhau 2 π : α vaø 2 π sin cos 2 cos sin 2 tg cot g 2 cot g tg 2 π +α = α π +α =− α π α π +α =− α
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f. () ( ) ( ) +π=− +π= k k sin x k 1 sin x,k Z cos x k 1 cosx,k Z tg x k tgx,k Z cot g x k cot gx V. Coâng thöùc coäng ( ) sin a b sinacosb sin bcosa cos a b cosacos b sin asin b tga tgb tg a b 1t g a t g b ±= ± ± m m VI. Coâng thöùc nhaân ñoâi = =− = = = = 22 2 2 2 2 sin2a 2sinacosa cos2a cos a sin a 1 2sin a 2cos a 1 2tga tg2a ga cot g a 1 cotg2a 2cotga VII. Coâng thöùc nhaân ba: 3 3 sin3a 3sin a 4sin a cos3a 4 cos a 3cosa VIII. Coâng thöùc haï baäc: 2 2 2 1 sin a 1 2 1 cos a 1 2 1c o s 2 a tg a o s 2 a =+ = + IX. Coâng thöùc chia ñoâi Ñaët a tt g 2 = (vôùi ak ) 2 ≠π+ π
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2 2 2 2 2t sina 1t cosa tga = + = + = X. Coâng thöùc bieán ñoåi toång thaønh tích () ab cosb 2cos cos 22 ab ab 2sin sin sina sinb sin sin b sin sin a b tga tgb cosacosb sin b a cot ga cot gb sina.sin b +− += −= ± ±= ± XI. Coâng thöùc bieån ñoåi tích thaønh toång ()() 1 cosa.cosb cos a b cos a b 2 1 sina.sin b cos a b cos a b 2 1 sina.cosb sin a b sin a b 2 =⎡ + + −⎤ ⎣⎦ + Baøi 1 : Chöùng minh 44 66 sin a cos a 1 2 sin a cos a 1 3 = Ta coù: ( ) 2 2 2 2 sin a cos a 1 sin a cos a 2sin acos a 1 = + = 2 Vaø: ( )( ) 4 2 24 2 2 sin a cos a 1 sin a cos a sin a sin acos a cos a 1 sin a cos a sin acos a 1 1 2 s i nac o sa s i o sa 1 3sin acos a = + + =+ =−
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Do ñoù: 44 2 2 66 2 2 sin a cos a 1 2sin acos a 2 sin a cos a 1 3sin acos a 3 +− == Baøi 2: Ruùt goïn bieåu thöùc () 2 2 1c o s x o s x A1 sin x sin x + + Tính giaù trò A neáu 1 cosx 2 =− vaø x 2 π < Ta coù: 22 2 o s xs i nx12 c o s xc o sx A sin x sin x ⎛⎞ ++ + = ⎜⎟ ⎝⎠ ( ) 2 21 co o s x A.
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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-Chuong1 - CHNG 1: CONG THC LNG GIAC I. nh ngha...

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