sin^ncos^n
y=sin^nx cos^nxy′=nsin^(n-1)xcosxcos^nx+ncos^(n-1)x(-sinx)sin^nx
=nsin^(n-1)xcos^(n-1)x(cos²x-sin²x)
=nsin^(n-1)xcos^(n-1)cos(2x)
绛旓細y=sin^nx cos^nx y鈥=nsin^(n-1)xcosxcos^nx+ncos^(n-1)x(-sinx)sin^nx =nsin^(n-1)xcos^(n-1)x(cos²x-sin²x)=nsin^(n-1)xcos^(n-1)cos(2x)
绛旓細n鍊嶈鍏紡锛氭牴鎹鎷夊叕寮(cos胃+isin胃)^n=cosn胃+isinn胃銆傚皢宸﹁竟鐢ㄤ簩椤瑰紡瀹氱悊灞曞紑鍒嗗埆鏁寸悊瀹為儴鍜岃櫄閮ㄥ彲浠ュ緱鍒颁笅闈袱缁勫叕寮 sin(n伪)=ncos^(n-1)伪路sin伪-C(n,3)cos^(n-3)伪路sin^3伪+C(n,5)cos^(n-5)伪路sin^5伪-鈥os(n伪)=cos^n伪-C(n,2)cos^(n-2)伪路sin^2伪+...
绛旓細绠鍗曡绠椾竴涓嬪嵆鍙紝绛旀濡傚浘鎵绀
绛旓細瑙ｏ細鈭sin[n蟺(l-t)/l]=sin[n蟺-(n蟺t)/l]=sin(n蟺)ncos(n蟺t/l)-cos(n蟺)sin(n蟺t/l)=[-(-1)^n]sin(n蟺t/l)锛屸埓sin[n蟺(l-t)/l]=[(-1)^(n+1)]sin(n蟺t/l)銆備緵鍙傝冦
绛旓細鍥犱负 [sin(nx)]'=ncos(nx)涓 [ncos(nx)]'=n*n[-sin(nx)]鎵浠 [sin(nx)]''=-n^2sin(nx)鍗 [sin(nx)]''+n^2sin(nx)=0 瀵逛簬sin(n*0)=sin(n*蟺)=0鍙互鏍规嵁浜屾鍑芥暟鐨勫浘鍍忓緱鍑
绛旓細n鍊嶈鍏紡 sin(n伪)=ncos^(n-1)伪路sin伪-C(n,3)cos^(n-3)伪路sin^3伪+C(n,5)cos^(n-5)伪路sin^5伪-鈥os(n伪)=cos^n伪-C(n,2)cos^(n-2)伪路sin^2伪+C(n,4)cos^(n-4)伪路sin^4伪-鈥﹀崐瑙掑叕寮 sin(伪/2)=卤鈭((1-cos伪)/2)cos(伪/2)=卤鈭((1+cos伪...
绛旓細y=sin^nx cos^nx y鈥=nsin^(n-1)xcosxcos^nx+ncos^(n-1)x(-sinx)sin^nx =nsin^(n-1)xcos^(n-1)x(cos²x-sin²x)=nsin^(n-1)xcos^(n-1)cos(2x)
绛旓細鍊嶈鍏紡锛歝os2胃=cos²胃-sin²胃=2cos²胃-1=1-2sin²胃锛1+cos2胃=2cos²胃 sin2胃=2sin胃cos胃 浠ｅ叆锛氬師寮=[2cos²胃+i2sin胃cos胃]^n =2^ncos^n(胃锛塠cos胃+isin胃]^n 娆ф媺鍏紡锛歝os螘+isin胃=e^i胃 [cos螘+isin胃]^n=e^in胃=cos...
绛旓細鐢ㄦ礇蹇呰揪娉曞垯鎴栬呴噸瑕佹瀬闄愩佺瓑浠锋棤绌峰皬閮藉彲銆傝繖閲岀敤鍚庤呰绠椾竴涓嬶細sinmx=(-1)^m脳sin(mx-m蟺)锛宻in(mx-m蟺)绛変环浜巑x-m蟺銆sinnx=(-1)^n脳sin(nx-n蟺)锛宻in(nx-n蟺)绛変环浜巒x-n蟺銆傛墍浠ワ紝鍘熸瀬闄=lim (-1)^(m-n)脳m(x-蟺)/n(x-蟺)=(-1)^(m-n)脳m/n ...
绛旓細sin(n伪)=ncos^(n-1)伪路sin伪-C(n,3)cos^(n-3)伪路sin^3伪+C(n,5)cos^(n-5)伪路sin^5伪-鈥 cos(n伪)=cos^n伪-C(n,2)cos^(n-2)伪路sin^2伪+C(n,4)cos^(n-4)伪路sin^4伪-鈥﹀崐瑙掑叕寮 sin(伪/2)=卤鈭((1-cos伪)/2) cos(伪/2)=卤鈭((1+cos伪)/2) ...
