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Luonggiac-Chuong1

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

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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 0 2 ≤ β ≤ π Ñaët k2 ,k Z α = β + π Ta ñònh nghóa: sin OK α = cos OH α = sin tg cos α α = α vôùi co s 0 α ≠ cos cot g sin α α = α vôùi sin 0 α ≠ II. Baûng giaù trò löôïng giaùc cuûa moät soá cung (hay goùc) ñaëc bieät Goùc α Giaù trò ( ) o 0 0 ( ) 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 || cotg α || 3 1 3 3 0 III. Heä thöùc cô baûn 2 2 sin cos 1 α + α = 2 2 1 1 tg cos + α = α vôùi ( ) k k Z 2 π α ≠ + π 2 2 1 t cotg sin + = α vôùi ( ) k k Z 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 ( ) ( ) cotg cotg −α = − α

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b. Buø nhau: vaø α π − α ( ) ( ) ( ) ( ) sin sin cos cos tg tg cotg cotg π − α = α π − α = − α π − α = − α π − α = − α c. Sai nhau : vaø π + π α α ( ) ( ) ( ) ( ) sin sin cos cos tg tg cotg cotg π + α = − α π + α = − α π + α = α π + α = α d. Phuï nhau: vaø α 2 π − α sin cos 2 cos sin 2 tg cotg 2 cotg tg 2 π − α = α π − α = α π − α = α π − α = α e.Sai nhau 2 π : α vaø 2 π + α sin cos 2 cos sin 2 tg cotg 2 cotg tg 2 π + α = α π + α = − α π + α = − α π + α = − α
f. ( ) ( ) ( ) ( ) ( ) ( ) + π = − + π = − + π = + π = k k sin x k 1 sinx,k Z cos x k 1 cosx,k Z tg x k tgx,k Z cotg x k cotgx V. Coâng thöùc coäng ( ) ( ) ( ) sin a b sinacosb sin bcosa cos a b cosacosb sinasin b tga tgb tg a b 1 tgatgb ± = ± ± = ± ± = m m VI. Coâng thöùc nhaân ñoâi = = = = = = 2 2 2 2 2 2 sin2a 2sinacosa cos2a cos a sin a 1 2sin a 2cos a 1 2tga tg2a 1 tg a cotg a 1 cotg2a 2cotga VII. Coâng thöùc nhaân ba: 3 3 sin3a 3sina 4sin a cos3a 4cos a 3cosa = = VIII. Coâng thöùc haï baäc: ( ) ( ) 2 2 2 1 sin a 1 cos2a 2 1 cos a 1 cos2a 2 1 cos2a tg a 1 cos2a = = + = + IX. Coâng thöùc chia ñoâi Ñaët a t tg 2 = (vôùi a k ) 2 ≠ π + π

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2 2 2 2 2t sina 1 t 1 t cosa 1 t 2t tga 1 t = + = + = X. Coâng thöùc bieán ñoåi toång thaønh tích ( ) ( ) a b a b cosa cosb 2cos cos 2 2 a b a b cosa cosb 2sin sin 2 2 a b a b sina sin b 2cos sin 2 2 a b a b sina sin b 2cos sin 2 2 sin a b tga tgb cosacosb sin b a cotga cotgb 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 4 4 6 6 sin a cos a 1 2 sin a cos a 1 3 + = + Ta coù: ( ) 2 4 4 2 2 2 2 2 sin a cos a 1 sin a cos a 2sin acos a 1 2sin acos a + = + = − 2 Vaø: ( )( ) ( ) 6 6 2 2 4 2 2 4 4 4 2 2 2 2 2 2 2 2 sin a
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Luonggiac-Chuong1 - CHNG 1 CONG THC LNG GIAC I nh ngha Tren...

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