arcsinsinx的原函数是什么 arcsin(sinx)等于什么
arcsinsinx\u7b49\u4e8e\u4ec0\u4e48?arcsinsinx\u7b49\u4e8ex\u3002
\u5206\u6790\u8fc7\u7a0b\u5982\u4e0b\uff1a
\u5047\u8bbex=30\u5ea6\uff0c\u5219sinx=1/2\u3002
arcsinsinx=arcsin1/2=30\u5ea6\u3002
\u7531\u6b64\u53ef\u5f97arcsinsinx=x\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0csinx\u8868\u793a\u7684\u662f\u6b63\u5f26\u51fd\u6570\u7684\u4e00\u4e2a\u503c\uff0c\u800carcsinsinx\u8868\u793a\u7684\u662fx\u8fd9\u4e2a\u89d2\u5ea6\u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u53cd\u6b63\u5f26\u51fd\u6570\uff08\u53cd\u4e09\u89d2\u51fd\u6570\u4e4b\u4e00\uff09\u4e3a\u6b63\u5f26\u51fd\u6570y=sinx\uff08x\u2208[-½\u03c0,½\u03c0]\uff09\u7684\u53cd\u51fd\u6570\uff0c\u8bb0\u4f5cy=arcsinx\u6216siny=x\uff08x\u2208[-1,1]\uff09\u3002\u7531\u539f\u51fd\u6570\u7684\u56fe\u50cf\u548c\u5b83\u7684\u53cd\u51fd\u6570\u7684\u56fe\u50cf\u5173\u4e8e\u4e00\u4e09\u8c61\u9650\u89d2\u5e73\u5206\u7ebf\u5bf9\u79f0\u53ef\u77e5\u6b63\u5f26\u51fd\u6570\u7684\u56fe\u50cf\u548c\u53cd\u6b63\u5f26\u51fd\u6570\u7684\u56fe\u50cf\u4e5f\u5173\u4e8e\u4e00\u4e09\u8c61\u9650\u89d2\u5e73\u5206\u7ebf\u5bf9\u79f0\u3002
\u5728\u6570\u5b66\u4e2d\uff0c\u53cd\u4e09\u89d2\u51fd\u6570\uff08\u5076\u5c14\u4e5f\u79f0\u4e3a\u5f13\u5f62\u51fd\u6570\uff08arcus functions\uff09\uff0c\u53cd\u5411\u51fd\u6570\uff08antitrigonometric functions\uff09\u6216\u73af\u5f62\u51fd\u6570\uff08cyclometric functions\uff09\u662f\u4e09\u89d2\u51fd\u6570\u7684\u53cd\u51fd\u6570\uff08\u5177\u6709\u9002\u5f53\u7684\u9650\u5236\u57df\uff09\u3002
\u5177\u4f53\u6765\u8bf4\uff0c\u5b83\u4eec\u662f\u6b63\u5f26\uff0c\u4f59\u5f26\uff0c\u6b63\u5207\uff0c\u4f59\u5207\uff0c\u6b63\u5272\u548c\u8f85\u52a9\u51fd\u6570\u7684\u53cd\u51fd\u6570\uff0c\u5e76\u4e14\u7528\u4e8e\u4ece\u4efb\u4f55\u4e00\u4e2a\u89d2\u5ea6\u7684\u4e09\u89d2\u6bd4\u83b7\u5f97\u4e00\u4e2a\u89d2\u5ea6\u3002 \u53cd\u4e09\u89d2\u51fd\u6570\u5e7f\u6cdb\u5e94\u7528\u4e8e\u5de5\u7a0b\uff0c\u5bfc\u822a\uff0c\u7269\u7406\u548c\u51e0\u4f55\u3002
\u5f53x\u5c5e\u4e8e[\uff0d\u03c0/2\uff0c\u03c0/2]\uff0carcsin\uff08sinx\uff09=x
\u5f53x\u4e0d\u5c5e\u4e8e[\uff0d\u03c0/2\uff0c\u03c0/2]\uff0carcsin\uff08sinx\uff09=x0
\u5176\u4e2dx0=x+2k\u03c0\uff0c\u8981\u6c42x0\u4e0ex\u540c\u53f7\u4e14\u2460\u82e5x\u4e3a\u6b63\uff0cx0\u4e3a\u80fd\u53d6\u5230\u7684\u6700\u5c0f\u503c\u2461\u82e5x\u4e3a\u8d1f\uff0c\u5219x0\u4e3a\u80fd\u53d6\u5230\u7684\u6700\u5927\u503c
\u8bc1\u660e\uff1a \u56e0\u4e3asinx\u7684\u5b9a\u4e49\u57df\u4e3aR\uff0c\u503c\u57df\u4e3a\u3010-1\uff0c1\u3011\uff0c\u7531\u53cd\u51fd\u6570\u7684\u6027\u8d28\u53ef\u77e5sinx\u5728\u6574\u4e2a\u5b9e\u6570\u96c6\u6ca1\u6709\u53cd\u51fd\u6570\uff0c\u53d6sinx\u9760\u8fd1\u539f\u70b9\u7684\u4e00\u4e2a\u5468\u671f\u533a\u95f4[\uff0d\u03c0/2\uff0c\u03c0/2]\uff0c\u5728\u8fd9\u4e2a\u533a\u95f4sinx\u6709\u53cd\u51fd\u6570arcsinx\u3002\u6545arcsinx\u7684\u5b9a\u4e49\u57df\u4e3a\u3010-1\uff0c1\u3011,\u503c\u57df\u4e3a[\uff0d\u03c0/2\uff0c\u03c0/2]
arcsinx\u7684\u5bf9\u8c61\u662f\u5728\u95ed\u533a\u95f4\u3010-1\uff0c1\u3011\u7684\u5b9e\u6570\uff0c\u800csinx\u7684\u5bf9\u8c61\u662f\u4ee5\u201c\u00b0\u201d\u4e3a\u5355\u4f4d\u7684\u6570\u3002
\u62d3\u5c55\uff1a
y=e^x\u548cy=lnx\u4e92\u4e3a\u53cd\u51fd\u6570\u3002
令t=sinx,代入积分得1/2(arcsinsinx)^2,你求导试一试，其已验证，正确，请及时采纳
函数arcsinsinx=x,其定义域为R,值域为〔-π/2,π/2〕
绛旓細鍘熷嚱鏁颁负:sinx
绛旓細鐢辨鍙緱arcsinsinx=x锛屼篃灏辨槸璇达紝sinx琛ㄧず鐨勬槸姝ｅ鸡鍑芥暟鐨勪竴涓硷紝鑰宎rcsinsinx琛ㄧず鐨勬槸x杩欎釜瑙掑害銆
绛旓細arcsinx鐨勫師鍑芥暟鏄痵inx銆傝缁嗚В閲婂涓嬶細涓銆佸師鍑芥暟涓庡弽鍑芥暟鐨勬蹇 鍦ㄥ井绉垎瀛︿腑锛屽師鍑芥暟涓庡弽鍑芥暟鏄竴瀵圭浉浜掗嗙殑鍑芥暟銆傜粰瀹氫竴涓嚱鏁皔=f锛屽鏋滃瓨鍦ㄥ彟涓涓嚱鏁癵锛屼娇寰梖鍜実浜掍负鍙嶅嚱鏁帮紝鍗砯鐨勪綔鐢ㄨ兘鎶垫秷g鐨勪綔鐢紝鍒欐垜浠f鍜実浜掍负鍘熷嚱鏁板拰鍙嶅嚱鏁板叧绯汇備簩銆乤rcsinx涓巗inx鐨勫叧绯 arcsinx鏄寮﹀嚱鏁皊inx...
绛旓細I = 鈭 arcsinx dx = x arcsinx - 鈭 [x/鈭(1-x^2)] dx = x arcsinx + (1/2) 鈭 [1/鈭(1-x^2)] d(1-x^2) = x arcsinx + 鈭(1-x^2) +C I = 鈭 arccosx dx = x arccosx + 鈭 [x/鈭(1-x^2)] dx = x arccosx - (1/2) 鈭 [1/鈭(1-x^2)] d...
绛旓細arcsin(sinx)涓嶄竴瀹氱瓑浜巟锛屾槸鏈夋潯浠剁殑銆傝繖鏄洜涓篴rcsinx鐨勫畾涔夊煙鏄蓟-1,1锛斤紝涔熷氨鏄痵inx鐨勫煎煙鏄蓟-1,1锛姐傛墍浠ュ湪闂尯闂碵-蟺/2,蟺/2]涓婏紝arcsin(sinx)涓巟鐩稿悓銆傜敤鏁板璇█琛ㄨ揪鐨勮瘽锛屾湁浠ヤ笅缁撹:鑻rcsin(sinx)=a,鍒檃鈭圼-蟺/2,蟺/2],涓攕ina=sinx銆傚綋x鈭圼-蟺/2,蟺/2]鏃,arcsin(...
绛旓細鑻ョ湅涓嶆竻锛屽彲鐐瑰嚮鏀惧ぇ銆
绛旓細arcsinx鐨勫師鍑芥暟鍙互鐢ㄥ垎閮ㄧН鍒嗘硶杩涜姹傝В锛屽叿浣撹繃绋嬪涓嬶細鈭玜rcsinxdx =xarcsinx-鈭玿(arcsinx)'dx =xarcsinx-鈭玿/鈭氾紙1-x²)dx =xarcsinx-1/2鈭1/鈭氾紙1-x²)d(x²-1)=xarcsinx+1/2鈭1/鈭氾紙1-x²)d(1-x²)=xarcsinx+鈭氾紙1-x²)/2+C 鎵浠...
绛旓細鈭玜rcsinxdx =xarcsinx-鈭玿(arcsinx)'dx =xarcsinx-鈭玿/鈭(1-x²)dx =xarcsinx-1/2鈭1/鈭(1-x²)d(x²-1)=xarcsinx+1/2鈭1/鈭(1-x²)d(1-x²)=xarcsinx+鈭(1-x²)/2+C 鍙嶆寮﹀嚱鏁帮紙鍙嶄笁瑙掑嚱鏁颁箣涓锛変负姝ｅ鸡鍑芥暟y=sinx锛坸鈭圼-½...
绛旓細鑻ョ湅涓嶆竻锛屽彲鐐瑰嚮鏀惧ぇ銆
绛旓細arcsinx1/2鐨勫師鍑芥暟鏄細arcsin鐨勫師鍑芥暟涓簊inx銆傚嚱鏁扮殑瀹氫箟閫氬父鍒嗕负浼犵粺瀹氫箟鍜岃繎浠ｅ畾涔夛紝鍑芥暟鐨勪袱涓畾涔夋湰璐ㄦ槸鐩稿悓鐨勶紝鍙槸鍙欒堪姒傚康鐨勫嚭鍙戠偣涓嶅悓锛屼紶缁熷畾涔夋槸浠庤繍鍔ㄥ彉鍖栫殑瑙傜偣鍑哄彂銆
