问个微积分问题（关于sin和cos的）详情请入内。 cos(7x)dx微积分
\u8bf7\u95ee\u8fd9\u4e2a\u5fae\u79ef\u5206\u9898\u76ee\u4e3a\u4f55\u8fd8\u9700\u8981\u6362\u6210sin\u548ccos\u624d\u80fd\u8bc1\u660e\uff1f\u56e0\u4e3a\u8fd9\u4e24\u4e2a\u5728\u4e66\u4e0a\u7684\u7b2c3\u8282\u8bc1\u660e\u8fc7\u4e86\uff0c\u53ef\u4ee5\u5f53\u7ed3\u8bba\u7528\u3002\u800ctan\u4e4b\u524d\u8fd8\u6ca1\u6709\u63d0\u5230\u8fc7\u3002
cos(2npi)=1 cos[(2n+1)pi]=-1 sin(npi)=0 cos(npi+pi/2)=0 sin(2npi+pi/2)=1 sin[(2n+1)pi+pi/2]=-1 cospi= -1,sinpi= 0 sin4pi=0, cos4pi=1 sinpi/2=1, cospi/2=0 sinpi/4=\u4e8c\u5206\u4e4b\u6839\u53f72 cospi/4=\u4e8c\u5206\u4e4b\u6839\u53f72
SIN60=COS30=（√3）/2SIN45=COS45=（√2）/2
SIN30=COS60=1/2
TAN30=COT60=（√3）/3
TAN45=COT45= 1
TAN60=COT30= √3
SIN90=1
COS90=0
当然，针对你的问题，π/3就是60°，π/6是30°，没有π/5的公式吧？
所以sinpi/3= （√3）/2 ，cospi/3=1/2
sinpi/3=根号(3)/2 cospi/3=1/2
sinpi/5=(根号（5）-1)/4 cospi/5=(1+根号（5）)/4
依次等于0.5 ,根3/2 ,0.5*Sqrt(0.5*Sqrt(5-Sqrt(5))),(1+根5)/4
绛旓細SIN30=COS60=1/2 TAN30=COT60=锛堚垰3锛/3 TAN45=COT45= 1 TAN60=COT30= 鈭3 SIN90=1 COS90=0 褰撶劧锛岄拡瀵逛綘鐨闂锛屜/3灏辨槸60掳锛屜/6鏄30掳锛屾病鏈壪/5鐨勫叕寮忓惂锛熸墍浠sinpi/3= 锛堚垰3锛/2 锛宑ospi/3=1/2
绛旓細sin4pi=0, cos4pi=1 sinpi/2=1, cospi/2=0 sinpi/4=浜屽垎涔嬫牴鍙2 cospi/4=浜屽垎涔嬫牴鍙2
绛旓細鏂规硶濡備笅锛岃浣滃弬鑰冿細
绛旓細鈭竎os胃d胃=鈭竏(sin胃)=胃sin胃-鈭玞os胃d胃=胃sin胃+cos胃+c(c涓轰换鎰忓父鏁)
绛旓細cosx鐨绉垎绛変簬sinx+C锛岃繖鏄熀鏈Н鍒嗗叕寮忥紝鍥犱负涓嶅畾绉垎鏄鏁拌繍绠楃殑閫嗚繍绠楋紝姹俢osx鐨勪笉瀹氱Н鍒嗗氨鏄眰璋佺殑瀵兼暟绛変簬cosx锛屽洜涓(sinx+C)'=cosx锛屾墍浠モ埉cosxdx=sinx+C銆備笁瑙掑嚱鏁扮Н鍒嗗叕寮忔槸锛sin(伪锛嬑诧紜纬锛夛紳sin伪路cos尾路cos纬锛媍os伪路sin尾路cos纬锛媍os伪路cos尾路sin纬锛峴in伪路sin尾路sin...
绛旓細浣犵殑绛旀涓 (1/2)sin^2-(1/4)sin^4 =(1/4)*sin^2*(2-sin^2)=(1/4)sin^2+(1/4)sin^2cos^2 =(1/4)sin^2+(1/4)cos^2-(1/4)cos^4 (1/4)-(1/4)cos^4 鍥犱负C浠ｈ〃浠绘剰鏁帮紝鎵浠(1/4)鍙互褰掑苟鍏锛屾墍浠ヤ綘鐨勭瓟妗堝拰涔︿笂鐨勬槸绛変环鐨勩傛棰樺彲浠ヨ繖涔堝仛 -鈭玞os^3dcos=-...
绛旓細瀵sin(x)杩涜绉垎寰楀埌-cos(x) + C锛岀劧鍚庡湪鍖洪棿[0, π/2]涓婅繘琛屾眰鍊硷紝寰楀埌-cos(π/2) + C - (-cos(0) + C) = 1銆傛讳箣锛屼笁瑙掑嚱鏁扮殑绉垎鍏紡鏄寰Н鍒涓殑閲嶈鍐呭涔嬩竴锛屽畠浠笉浠呭彲浠ュ府鍔╂垜浠眰瑙ｆ秹鍙婁笁瑙掑嚱鏁扮殑绉垎闂锛岃繕鍙互甯姪鎴戜滑鏇存繁鍏ュ湴鐞嗚В涓夎鍑芥暟鍜屽井绉垎鐨勬ц川鍜屽師鐞嗐
绛旓細璨屼技妤间笂鐨勯兘绠楅敊浜嗗惂 锛
绛旓細(10)=鈭垰(4-(x+1)²)dx鎹㈠厓x=2sinu-1 =鈭2cosud(2sinu-1)=2鈭(cos2u+1)du=sin2u+2u+C =(x+1)鈭(4-(x+1)²)/2+2arcsin((x+1)/2)+C (11)鎹㈠厓³鈭歺=u锛宒x=3u²du =鈭3u²sinudu=-3鈭玼²dcosu=-3u²cosu+3鈭玞osudu²...
绛旓細(2)寰Н鍒甯哥敤鍏紡锛欴x sin x=cos x cos x = -sin x tan x = sec2 x cot x = -csc2 x sec x = sec x tan x csc x = -csc x cot x sin x dx = -cos x + C cos x dx = sin x + C tan x dx = ln |sec x | + C cot x dx = ln |sin x | + C sec ...
