高一诱导公式 高一数学 诱导公式
\u9ad8\u4e00\u6570\u5b66\u8bf1\u5bfc\u516c\u5f0f\u65b9\u6cd51 \u500d\u89d2\u516c\u5f0f\u6cd5+\u8bf1\u5bfc\u516c\u5f0f\uff1a\u5206\u6bcd=\u30142sin\uff08\u03c0/4\uff0da/2\uff09sin\uff08\u03c0/4\uff0ba/2\uff09\u3015 = sin2\uff08\u03c0/4\uff0da/2\uff09 = sin\uff08\u03c0/2\uff0da\uff09 = cos a;\u539f\u5f0f= sina / cosa =tana \u65b9\u6cd52 \u548c\u5dee\u89d2\u516c\u5f0f+\u4e8c\u500d\u89d2\u516c\u5f0f\u5206\u6bcd=\u30142sin\uff08\u03c0/4\uff0da/2\uff09sin\uff08\u03c0/4\uff0ba/2\uff09\u3015 =2( sin\u03c0/4cosa/2-cos\u03c0/4 sina/2 ) ( sin\u03c0/4cosa/2+cos\u03c0/4 sina/2 ) =2 (\u6839\u53f72/2) ( cosa/2- sina/2 )(\u6839\u53f72/2) ( cosa/2+ sina/2 ) = cos^2 a/2 - sin^2 a/2 =cosa;\u539f\u5f0f= sina / cosa =tana \u65b9\u6cd53 \u548c\u5dee\u89d2\u5316\u79ef\u56e0\u4e3a cos [\uff08\u03c0/4\uff0da/2) +\uff08\u03c0/4\uff0ba/2\uff09] =0= = cos\uff08\u03c0/4\uff0da/2\uff09cos\uff08\u03c0/4\uff0ba/2\uff09-sin\uff08\u03c0/4\uff0da/2\uff09sin\uff08\u03c0/4\uff0ba/2\uff09 cos [\uff08\u03c0/4\uff0da/2) -\uff08\u03c0/4\uff0ba/2\uff09] =cosa= = cos\uff08\u03c0/4\uff0da/2\uff09cos\uff08\u03c0/4\uff0ba/2\uff09+sin\uff08\u03c0/4\uff0da/2\uff09sin\uff08\u03c0/4\uff0ba/2\uff09\u4e0a\u9762\u4e24\u5f0f\u5b50\u76f8\u51cf\uff1acosa=2 sin\uff08\u03c0/4\uff0da/2\uff09sin\uff08\u03c0/4\uff0ba/2\uff09\u539f\u5f0f= sina / cosa =tana
错题
绛旓細鍥犱负锛宻in²x + cos²x = 1 锛屽張锛宑os(蟺/4 + 伪)= sin[蟺/2 - (蟺/4 + 伪)]= sin(蟺/4 - 伪) 锛屾墍浠ワ紝cos²(蟺/4 - 伪) + cos²(蟺/4 + 伪)= cos²(蟺/4 - 伪) + sin²(蟺/4 - 伪)= 1 ...
绛旓細璇卞鍏紡鐨勬湰璐 鎵璋撲笁瑙掑嚱鏁拌瀵煎叕寮忥紝灏辨槸灏嗚n路(蟺/2)卤伪鐨勪笁瑙掑嚱鏁拌浆鍖栦负瑙捨辩殑涓夎鍑芥暟銆傚父鐢ㄧ殑璇卞鍏紡 鍏紡涓锛 璁疚变负浠绘剰瑙掞紝缁堣竟鐩稿悓鐨勮鐨勫悓涓涓夎鍑芥暟鐨勫肩浉绛夛細sin锛2k蟺+伪锛=sin伪 k鈭坺 cos锛2k蟺+伪锛=cos伪 k鈭坺 tan锛2k蟺+伪锛=tan伪 k鈭坺 cot锛2k蟺+伪锛=cot伪 ...
绛旓細鎺ㄧ畻鍏紡锛3蟺/2 卤 伪涓幬辩殑涓夎鍑芥暟鍊间箣闂寸殑鍏崇郴锛歴in锛3蟺/2+伪锛=锛峜os伪 sin锛3蟺/2锛嵨憋級=锛峜os伪 cos锛3蟺/2+伪锛=sin伪 cos锛3蟺/2锛嵨憋級=锛峴in伪 tan锛3蟺/2+伪锛=锛峜ot伪 璇卞鍏紡璁板繂鍙h瘈锛氣滃鍙樺伓涓嶅彉锛岀鍙风湅璞¢檺鈥濄傗滃銆佸伓鈥濇寚鐨勬槸蟺/2鐨勫嶆暟鐨勫鍋讹紝鈥滃彉涓...
绛旓細cos(3/2蟺+蟺/4)=-cos(1/2蟺+蟺/4)=-锛-sin蟺/4)=sin蟺/4
绛旓細濂囧彉鍋朵笉鍙樼鍙风湅璞¢檺鏄楂樹竴骞寸骇瀛︾殑涓夎鍑芥暟鐨璇卞鍏紡銆傚鍙樺伓涓嶅彉锛堝k鑰岃█锛屾寚k鍙栧鏁版垨鍋舵暟锛夛紝绗﹀彿鐪嬭薄闄愶紙鐪嬪師鍑芥暟锛屽悓鏃跺彲鎶娢辩湅鎴愭槸閿愯锛夈傚叕寮忓彸杈圭殑绗﹀彿涓烘妸伪瑙嗕负閿愯鏃讹紝瑙択路360掳+伪锛坘鈭圸锛夛紝-伪銆180掳卤伪锛360掳-伪鎵鍦ㄨ薄闄愮殑鍘熶笁瑙掑嚱鏁板肩殑绗﹀彿鍙蹇嗭細涔濆崄搴﹁璇卞鍚嶄笉...
绛旓細璇佹槑锛氬洜f(cosx)=cos17x.浠=(蟺/2)-t.===>cosx=cos[(蟺/2)-t]=sint.cos17x=cos[(17蟺/2)-17t]=cos[8蟺+(蟺/2)-17t]=cos[(蟺/2)-17t]=sin17t.鏁協(cosx)=f[cos(蟺/2-t)]=cos[(17蟺/2)-17t].===>f(sint)=sin17t.鍗砯(sinx)=sin17x.
绛旓細闃垮皵娉曟槸绗洓璞¢檺瑙掞紝閭d箞cos(闃垮皵娉+2鍒嗕箣娲)鏄涓璞¢檺瑙.鍥犱负cos闃垮皵娉=1/5.鎵浠ョ涓璞¢檺鍜岀鍥涜薄闄怌os鍊奸兘鏄鐨.鎵浠os(闃垮皵娉+2鍒嗕箣娲撅級=1/5
绛旓細(浠ヤ笂k鈭圸)涓鑸殑鏈甯哥敤鍏紡:鍙h瘈:濂囧彉鍋朵笉鍙橈紝绗﹀彿鐪嬭薄闄 Sin(A+B)=SinA*CosB+SinB*CosA Sin(A-B)=SinA*CosB-SinB*CosA Cos(A+B)=CosA*CosB-SinA*SinB Cos(A-B)=CosA*CosB+SinA*SinB Tan(A+B)=(TanA+TanB)/(1-TanA*TanB)绗2/4椤 Tan(A-B)=(TanA-TanB)/(1+TanA*TanB)...
绛旓細sin锛坅-3蟺锛=2cos(a-4蟺锛夊彲鍖栦负sin锛4蟺+a-3蟺锛=2cos(4蟺+a-4蟺锛夊嵆sin锛埾+a)=-sina=2cosa [sin锛埾-a)+5cos(2蟺-a)]/[2sin(3蟺/2-a)-sin(-a) ]=[sina+5cosa]/[-2cosa+sina]=3cosa/-4cosa=-3/4
绛旓細cos锛埾-a锛=cos锛坅-蟺锛=-cosa sin锛埾-a锛=-sin锛坅-蟺锛=sina tan锛埾-a锛=-tan锛坅-蟺锛=-tana