sin2x为什么等于2sinxcosx?
sin2x等于2sinxcosx。这其实是由两角和的正弦公式sin(x+y)=sinxcosy+cosxsiny得到。此外，还有几个三角恒等式cos(x+y)=cosxcosy-sinxsinycos(x-y)=cosxcosy+sinxsinysin(x-y)=sinxcosy-cosxsinytan(x+y)=(tanx+tany)/(1-tanxtany)tan(x-y)=(tanx-tany)/(1+tanxtany)想推导出各种二倍角公式，只需将和角公式中的y替换为x即可。
sin2x的取值范围
函数y=sin2x是正弦函数，它的自变量的取值范围是全体实数，它的值域是-1到1，它的导函数应区分外层与内层函数分别求导尔后求积。那么我们知道，它的外层函数的导数是cos2x，它的内层函数是2x，它的导数是2，那么原函数的导数就是等于2cos2x。
绛旓細鎸夌収鍏紡鏉ヨ锛sin2x=2sinxcosx锛屽綋x=2k蟺,锛坘鏄暣鏁帮級鏃讹紝cosx=1锛屾鏃秙in2x =2sinx鎴愮珛 褰搙->0鏄sinx/x鐨勬瀬闄愭槸1锛岃繖涓瘉鏄庨渶瑕佺敤鍒板す閫煎畾鐞嗭紝鍙互鍥涘垎涔嬩竴鍗曚綅鍦嗕綔鍥撅紙鍥剧暐锛夛紝鐒跺悗鎵惧嚭sinx锛宼anx锛岄氳繃鎺ㄥ鍙互璇佸嚭cosx<sinx/x<1锛岃宑osx鐨勬瀬闄愶紙x瓒嬩簬0锛夋槸1锛屾牴鎹す閫煎畾鐞嗗緱sinx/x瓒嬩簬...
绛旓細sin2x鍜2sinx杞崲鎶宸э細鐢眂os2x=(cosx)^2-(sinx)^2锛屽緱(sinx)^2=(1-cos2x)/2锛岀敱sin2x=2sinxcosx锛屽緱(sinx)^2={1-鈭歔1-(sin2x)^2]}/2sin2x=2sinxcosx锛(sin2x)/2=sinxcosx锛屽彧鏈塩osx=1鏃讹紝sin2x鎵绛変簬sinx銆傜幇浠ｆ寮﹀叕寮忔槸锛歴in=鐩磋涓夎褰㈢殑瀵硅竟姣旀枩杈广傛枩杈逛负r锛屽杈逛负y锛...
绛旓細sin 鏄釜鍑芥暟锛 涓嶆槸鏁存暟褰㈠紡鐨 锛屾墍浠inx 鏄釜鏁 杩欐牱 sin2x 鏄2鍊嶇殑x瑙 2sinx 鏄2鍊峴inx 涔熷氨鏄sin2x 鏄2鍊峹瑙掔殑sin鍊 鑰2sinx 鏄2鍊嶇殑sinx鍊 宸埆寰堝ぇ鐨勶紝浣嗘槸鍙互鐩镐簰杞崲
绛旓細sin2x=2sinxcosx銆傚垎鏋愯繃绋嬪涓嬶細sin(伪+尾)=sin伪cos尾+ sin尾cos伪 sin(伪-尾)=sin伪cos尾-sinB*cos伪 鏍规嵁sin(伪+尾)=sin伪cos尾+ sin尾cos伪鍙緱锛歴in2x=sin锛坸+x锛=sinxcosx+sinxcosx=2sinxcosx
绛旓細sin2x=2sinxcosx 杩欏叾瀹炴槸鐢变袱瑙掑拰鐨勬寮﹀叕寮锛岀敱sin锛坸+y锛=sinxcosy+cosxsiny 寰楀埌銆傛澶,杩樻湁鍑犱釜涓夎鎭掔瓑寮忥細cos锛坸-y锛=cosxcosy+sinxsiny sin锛坸-y锛=sinxcosy-cosxsiny 鎯虫帹瀵煎嚭鍚勭浜屽嶈鍏紡锛屽彧闇灏嗗拰瑙掑叕寮忎腑鐨剏鏇挎崲涓簒鍗冲彲銆傛敞鎰忥細涓よ鍜屽樊鐨勬鍒囧叕寮忓繀椤诲湪绛夊紡涓よ竟閮芥湁鎰忎箟鏃舵柟鍙...
绛旓細sin2x绛変簬2sinxcosx銆傝繖鍏跺疄鏄敱涓よ鍜岀殑姝ｅ鸡鍏紡sin(x+y)=sinxcosy+cosxsiny寰楀埌銆傛澶栵紝杩樻湁鍑犱釜涓夎鎭掔瓑寮廲os(x+y)=cosxcosy-sinxsinycos(x-y)=cosxcosy+sinxsinysin(x-y)=sinxcosy-cosxsinytan(x+y)=(tanx+tany)/(1-tanxtany)tan(x-y)=(tanx-tany)/(1+tanxtany)鎯虫帹瀵煎嚭鍚勭浜...
绛旓細sin2x=sin (x+x)=sinxcosx+cosxsinx =2sinxcosx
绛旓細2x=x+x sin2x=sin(x+x)姝ｅ鸡涓よ鍜屽叕寮忥細sin(a+b)=sinacosb+cosasinb 鎵浠in(x+x)=sinxcosx+cosxsinx=2sinxcosx
绛旓細(1/2)sin2x銆備竴銆佷緷鎹細鍊嶈鍏紡锛歴in2x=2sinxcosx 浜屻佸嶈鍏紡鎺ㄥ锛氬洜涓簊in(A+B)=sinAcosB+cosAsinB锛堜笁瑙掑嚱鏁帮級鎵浠in2A=2sinAcosA 涓夈佹敞锛氫笁瑙掑嚱鏁扮殑鎺ㄥ锛氶鍏堝缓绔嬬洿瑙掑潗鏍囩郴,鍦ㄧ洿瑙掑潗鏍囩郴xOy涓綔鍗曚綅鍦哋,骞朵綔鍑鸿a,b,涓-b,浣胯a鐨勫紑杈涓Ox,浜ゅ渾O浜庣偣P1,缁堣竟浜ゅ渾O浜庣偣P2,瑙抌...
绛旓細sin2x=2sinxcosx锛(sin2x)/2=sinxcosx锛屽彧鏈塩osx=1鏃讹紝sin2x鎵绛変簬sinx銆
