正弦函数和余弦函数在区间0到∏所围成的面积 正弦曲线y=sinx与余弦曲线y=cosx及直线x=0和直线...
\u8ba1\u7b97\u6b63\u5f26\u66f2\u7ebfy=sin x\uff0c\u5728(0,\u03c0\uff09\u4e0a\u4e0ex\u8f74\u6240\u56f4\u6210\u90e8\u5206\u7684\u9762\u79ef\u3002\u6240\u6c42\u9762\u79ef=\u222bsinxdx
=(-cosx)|
=2.
\u6211\u4e0d\u4f1a\u622a\u56fe\uff0c\u60a8\u81ea\u5df1\u753b\u56fe\uff0c\u53ef\u4ee5\u5417\uff1f
\u5982\u56fe\uff0c\u56e0\u4e3a\u5728\u533a\u95f4\uff080\uff0c\uff09\u4e0a\uff0c\u6b63\u5f26\u66f2\u7ebfy=sinx\u4e0e\u4f59\u5f26\u66f2\u7ebfy=cosx\u5728x= \u03c0 4 \u5904\u6709\u4ea4\u70b9\uff08 \u03c0 4 \uff0c 2 2 \uff09\u2234\u6240\u6c42\u56f4\u6210\u533a\u57df\u7684\u9762\u79ef\u4e3aS= \u222b \u03c0 4 0 (cosx-sinx)dx + \u222b \u03c0 \u03c0 4 (sinx-cosx)dx =\uff08sinx+cosx\uff09 | \u03c0 4 0 +\uff08-cosx-sinx\uff09 | \u03c0 \u03c0 4 =[\uff08 2 2 + 2 2 \uff09-\uff080+1\uff09]+[\uff081-0\uff09-\uff08- 2 2 - 2 2 \uff09]=2 2 \u6545\u7b54\u6848\u4e3a\uff1a 2 2
S₁=2∫(π/2,0)cosxdx=2sin(x)|(π/2,0)=2
S₂=∫(π,0)sinxdx=-cos(x)|(π,0)=2
S₃=∫(π/4,0)sinxdx=-cos(x)|(π/4,0)=1-√2/2
S₄=∫(π/2,π/4)cosxdx=sin(x)|(π/2,π/4)=1-√2/2
∴S=4-2+√2=2+√2
绛旓細S₁=2鈭(蟺/2,0)cosxdx=2sin(x)|(蟺/2,0)=2 S₂=鈭(蟺,0)sinxdx=-cos(x)|(蟺,0)=2 S₃=鈭(蟺/4,0)sinxdx=-cos(x)|(蟺/4,0)=1-鈭2/2 S₄=鈭(蟺/2,蟺/4)cosxdx=sin(x)|(蟺/2,蟺/4)=1-鈭2/2 鈭碨=4-2+鈭2=2+鈭2 ...
绛旓細f(x)=sinx鍦0鍒扳垙涓婄殑骞冲潎鍊间负2/蟺銆備竴鑸殑锛屽湪鐩磋鍧愭爣绯讳腑锛岀粰瀹氬崟浣嶅渾锛屽浠绘剰瑙捨憋紝浣胯伪鐨勯《鐐逛笌鍘熺偣閲嶅悎锛屽杈逛笌x杞撮潪璐熷崐杞撮噸鍚堬紝缁堣竟涓庡崟浣嶅渾浜や簬鐐筆锛坲锛寁锛夛紝閭ｄ箞鐐筆鐨勭旱鍧愭爣v鍙仛瑙捨辩殑姝ｅ鸡鍑芥暟锛岃浣渧=sin伪銆傞氬父锛屾垜浠敤x琛ㄧず鑷彉閲忥紝鍗硏琛ㄧず瑙掔殑澶у皬锛岀敤y琛ㄧず鍑芥暟鍊硷紝杩...
绛旓細鐢卞浘璞＄殑澧炲噺鎬у彲鐭ワ細姝ｅ鸡鍑芥暟鍦[0,娲/2]鍐呮槸澧炲嚱鏁,鍦╗娲/2,娲綸涔嬮棿鏄噺鍑芥暟璁句笁瑙掑舰ABC涓,a,b,c鍒嗗埆鏄A,B,C鐨勫杈,a>ba/sinA=b/sinBa/b=sinA/sinB>1sinA>sinB褰撹A銆佽B涓病鏈夐挐瑙掓椂,瑙扐>瑙払褰撹A鏄挐瑙掓椂,瑙扐>瑙払濡傛灉瑙払鏄挐瑙,鍒檚inA>sinB=sin(180-B)瑙扐>180-B A+...
绛旓細鐢卞浘璞＄殑澧炲噺鎬у彲鐭ワ細姝ｅ鸡鍑芥暟鍦[0锛屾淳/2]鍐呮槸澧炲嚱鏁帮紝鍦╗娲/2锛屾淳]涔嬮棿鏄噺鍑芥暟 璁句笁瑙掑舰ABC涓紝a锛宐锛宑鍒嗗埆鏄A锛孊锛孋鐨勫杈癸紝a>b a/sinA=b/sinB a/b=sinA/sinB>1 sinA>sinB 褰撹A銆佽B涓病鏈夐挐瑙掓椂锛岃A>瑙払 褰撹A鏄挐瑙掓椂锛岃A>瑙払 濡傛灉瑙払鏄挐瑙掞紝鍒檚inA>sinB=sin(18...
绛旓細鍦ㄥ尯闂[0锛屜/3]涓婂崟璋冮掑锛屽湪鍖洪棿[蟺/3,蟺/2]锛堣繖鏄凡鐭ユ潯浠讹級鎵浠=蟺/3鏄痜(x)=sinwx鐨勬渶澶у肩偣锛岋紙杩欐槸鍗曡皟鍑芥暟鐨勬ц川鍐冲畾鐨勶紝涔熷氨鏄f(x)鍦▁=蟺/3鏃朵細鍙栧緱鏈澶у硷級鍗砯(蟺/3)=sin(w蟺/3)=1锛堝洜涓姝ｅ鸡鍑芥暟鏈澶у兼槸1锛夊嵆w蟺/3=蟺/2 +2k蟺锛坘涓烘暣鏁帮級锛堣繖鏄敱sin(w...
绛旓細x鈭堛0锛鈭銆峹/2-鈭/6鈭堛-鈭/6,鈭/3]鑷繁鐢讳釜浣欏鸡鍑芥暟鍥.鏈灏忓:2cos鈭/3=2*1/2=1
绛旓細鍦╗0锛屜/2],姝ｅ鸡鍑芥暟鍗曡皟閫掑 褰搙1=sinx x2=x鏃 x1<x2 鏈:sinx1<sinx2 鍗:sin(sinx)<sinx
绛旓細鑷劧涓嶇敤璇sin53掳=0.8 cos37掳=0.6 鍏蜂綋鎬庝箞璁板憿锛屽氨鏍规嵁绗竴璞￠檺鐨勮寰嬶紝姝ｅ鸡浠0~鈭/2锛屾槸閫掑鍖洪棿锛屼粠0~1锛浣欏鸡鏄粠1~0 涓婇潰 涔熷彲浠ユ帹锛屾牴鎹(sin伪)^2+(cos伪)^2=1 涓洪伩鍏嶈浼氾紝鎴戜笓闂ㄦ墦涓婃嫭鍙凤紝杩欎釜浣犲簲璇ュ緢鐔熸倝 鏍规嵁杩欎釜绠楋紝sin伪=卤0.8锛屽洜涓哄湪绗竴璞￠檺锛屾墍浠ュ彇姝ｏ紝sin伪=0...
绛旓細1銆姝ｅ鸡鍑芥暟鐨勫箓绾ф暟灞曞紑寮忥細 sinZ=Z危(n=0锝炩垶){[(-1)^n*Z^(2n)]/(2n+1)!}=Zf(Z) 娉細 (1)Z涓烘墍鏈夊鏁版椂锛岃绾ф暟閮芥敹鏁涳紝 (2)f(Z)鐨勬墍鏈夐浂鐐逛负c(n)=n蟺(n=卤1銆伮2銆佲︹β扁垶) 2銆佽f(Z,m)=危(n=0锝瀖){[(-1)^n*Z^(2n)]/(2n+1)!}锛 f(Z,m)鐨勬墍鏈...
绛旓細1.鐐光滅粯鍥锯啋缁樺埗鏂板嚱鏁扳啋sin锛坸锛夆2.鍙抽敭寰楀埌鐨姝ｅ鸡鍑芥暟锛岀偣鈥滃睘鎬р啋缁樺浘鈥濆湪鑼冨洿閲岄潰杈撳叆鈥0鈮鈮2pi鈥3.纭畾銆1.OK浜嗐傛敞锛氳緭鍏i鍑犱綍鐢绘澘浼氳嚜鍔ㄨ瘑鍒垚蟺鐨勩
