cos2π等于几 cosπ/5·cos2π/5等于多少？
\u6c42cos2\u03c0\u7b49\u4e8e\u591a\u5c11\u6c42\u6280\u5de7\u5177\u4f53\u56de\u7b54\u5982\u56fe\uff1a
\u8bbe\u03b1\u4e3a\u4efb\u610f\u89d2\uff0c\u7ec8\u8fb9\u76f8\u540c\u7684\u89d2\u7684\u540c\u4e00\u4e09\u89d2\u51fd\u6570\u7684\u503c\u76f8\u7b49\uff1a
sin\uff082k\u03c0+\u03b1\uff09=sin\u03b1 \uff08k\u2208Z\uff09
cos\uff082k\u03c0+\u03b1\uff09=cos\u03b1 \uff08k\u2208Z\uff09
tan\uff082k\u03c0+\u03b1\uff09=tan\u03b1 \uff08k\u2208Z\uff09
cot\uff082k\u03c0+\u03b1\uff09=cot\u03b1\uff08k\u2208Z\uff09
\u6269\u5c55\u8d44\u6599\uff1a
\u628a\u89d2\u03b1\u770b\u505a\u9510\u89d2\uff0c\u4e0d\u8003\u8651\u03b1\u89d2\u6240\u5728\u8c61\u9650\uff0c\u770bn\u00b7(\u03c0/2)\u00b1\u03b1\u662f\u7b2c\u51e0\u8c61\u9650\u89d2\uff0c\u4ece\u800c\u5f97\u5230\u7b49\u5f0f\u53f3\u8fb9\u662f\u6b63\u53f7\u8fd8\u662f\u8d1f\u53f7\u3002\u4ee5cos\uff08\u03c0/2+\u03b1\uff09=\uff0dsin\u03b1\u4e3a\u4f8b\uff0c\u7b49\u5f0f\u5de6\u8fb9cos\uff08\u03c0/2+\u03b1\uff09\u4e2dn=1\uff0c\u6240\u4ee5\u53f3\u8fb9\u7b26\u53f7\u4e3asin\u03b1\uff0c\u628a\u03b1\u770b\u6210\u9510\u89d2\uff0c\u6240\u4ee5\u03c0/2<\uff08\u03c0/2+\u03b1\uff09<\u03c0\uff0cy=cosx\u3002
\u4e09\u89d2\u51fd\u6570\u7684\u79ef\u5316\u548c\u5dee\u516c\u5f0f\uff1a
sin\u03b1 \u00b7 cos\u03b2=[sin(\u03b1 + \u03b2) + sin(\u03b1 - \u03b2)]/2
cos\u03b1 \u00b7 sin\u03b2=[sin(\u03b1 + \u03b2) - sin(\u03b1 - \u03b2)]/2
cos\u03b1 \u00b7 cos\u03b2=[cos(\u03b1 + \u03b2) + cos(\u03b1 - \u03b2)]/2
sin\u03b1 \u00b7 sin\u03b2= - [cos(\u03b1 + \u03b2) - cos(\u03b1 - \u03b2)]/2
\u5728\u6b63\u5207\u51fd\u6570\u7684\u56fe\u50cf\u4e2d\uff0c\u5728\u89d2k\u03c0 \u9644\u8fd1\u53d8\u5316\u7f13\u6162\uff0c\u800c\u5728\u63a5\u8fd1\u89d2 \uff08k+ 1/2\uff09\u03c0 \u7684\u65f6\u5019\u53d8\u5316\u8fc5\u901f\u3002\u6b63\u5207\u51fd\u6570\u7684\u56fe\u50cf\u5728 \u03b8 = \uff08k+ 1/2\uff09\u03c0 \u6709\u5782\u76f4\u6e10\u8fd1\u7ebf\u3002\u8fd9\u662f\u56e0\u4e3a\u5728 \u03b8 \u4ece\u5de6\u4fa7\u63a5\u8fdb \uff08k+ 1/2\uff09\u03c0 \u7684\u65f6\u5019\u51fd\u6570\u63a5\u8fd1\u6b63\u65e0\u7a77\uff0c\u800c\u4ece\u53f3\u4fa7\u63a5\u8fd1 \uff08k+ 1/2\uff09\u03c0 \u7684\u65f6\u5019\u51fd\u6570\u63a5\u8fd1\u8d1f\u65e0\u7a77\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1\u2014\u2014\u4e09\u89d2\u51fd\u6570\u8bf1\u5bfc\u516c\u5f0f
cos\u03c0/5*cos2\u03c0/5
=(2sin\u03c0/5*cos\u03c0/5*cos2\u03c0/5)/(2sin\u03c0/5)
=(sin2\u03c0/5*cos2\u03c0/5)/(2sin\u03c0/5)
=(2sin2\u03c0/5*cos2\u03c0/5)/2*(2sin\u03c0/5)
=sin4\u03c0/5/(4sin\u03c0/5)
=sin(\u03c0-\u03c0/5)/(4sin\u03c0/5)
=sin(\u03c0/5)/(4sin\u03c0/5)
=1/4
cos2π=3.1380872
cos2π=cos0=1
1
绛旓細SIN绯诲垪:sin蟺=0锛宻in2蟺=0锛宻in0=0锛宻in-蟺=0銆侰OS绯诲垪:cos蟺=-1锛cos2蟺=1锛宑os0=1锛宑os-蟺=-1銆傛牴鎹笁瑙掑嚱鏁拌瀵煎叕寮忥紙Induction formula锛夋帹婕斿嚭鏉ョ殑锛屽氨鏄皢瑙抧路(蟺/2)卤伪鐨勪笁瑙掑嚱鏁拌浆鍖栦负瑙捨辩殑涓夎鍑芥暟銆
绛旓細cos2蟺 =cos锛2蟺-2蟺锛=cos0 =1 鍦≧t鈻矨BC锛堢洿瑙掍笁瑙掑舰锛変腑锛屸垹C=90掳锛屸垹A鐨勪綑寮︽槸瀹冪殑閭昏竟姣斾笁瑙掑舰鐨勬枩杈癸紝鍗砪osA=b/c锛屼篃鍙啓涓篶osa=AC/AB銆備綑寮﹀嚱鏁帮細f(x)=cosx锛坸鈭圧锛夈俢os鍏紡鐨勫叾浠栬祫鏂欙細瀹冩槸鍛ㄦ湡鍑芥暟锛屽叾鏈灏忔鍛ㄦ湡涓2蟺銆傚湪鑷彉閲忎负2k蟺锛坘涓烘暣鏁帮級鏃讹紝璇ュ嚱鏁版湁鏋佸ぇ鍊...
绛旓細cos2蟺绛変簬1銆俢os鏄綑寮(浣欏鸡鍑芥暟)鐨勮〃杈惧紡锛屼笁瑙掑嚱鏁扮殑涓绉嶃備綑寮﹀嚱鏁版槸鍛ㄦ湡鍑芥暟锛屽叾鏈灏忔鍛ㄦ湡涓2蟺銆傚湪鑷彉閲忎负2k蟺(k涓烘暣鏁)鏃讹紝璇ュ嚱鏁版湁鏋佸ぇ鍊1锛涘湪鑷彉閲忎负(2k+1)蟺鏃讹紝璇ュ嚱鏁版湁鏋佸皬鍊-1銆傜敱姝ゅ彲鐭ワ紝cos2蟺=1銆俢os2蟺绛変簬澶氬皯 浣欏鸡(浣欏鸡鍑芥暟)锛屼笁瑙掑嚱鏁扮殑涓绉嶃傚湪Rt鈻矨BC(鐩磋涓夎褰...
绛旓細鍥犱负浣欏鸡鍑芥暟鐨勫懆鏈熶负360搴︼紝鎵浠360搴︾殑浣欏鸡鍊绛変簬0鐨勪綑寮﹀硷紝鍗崇瓑浜庘1鈥濄備綑寮︾殑瀹氫箟锛氬湪鐩磋涓夎褰腑锛岃鐨勯偦杈逛笌鏂滆竟鐨勬瘮鍊煎彨鍋氳繖涓鐨勪綑寮︺備綑寮﹀嚱鏁鏄涓夎鍑芥暟鐨勪竴绉嶏紝鍏跺畾涔夊煙鏄暣涓疄鏁伴泦锛屽煎煙鏄滈棴鍖洪棿涓婄殑璐熶竴鍒颁竴鈥濄傚畠鏄懆鏈熷嚱鏁帮紝鍏惰緝灏忔鍛ㄦ湡涓360搴︺備綑寮﹀嚱鏁版湁鏋佸ぇ鍊1锛屾湁鏋...
绛旓細cos2蟺=cos(2蟺+0)=cos0=1锛涘湪Rt鈻矨BC锛堢洿瑙掍笁瑙掑舰锛変腑锛屸垹C=90掳锛屸垹A鐨勪綑寮︽槸瀹冪殑閭昏竟姣斾笁瑙掑舰鐨勬枩杈癸紝鍗砪osA=b/c锛屼篃鍙啓涓篶osa=AC/AB銆備綑寮﹀嚱鏁帮細f(x)=cosx锛坸鈭圧锛夈
绛旓細绛変簬1鍟 浣欏鸡鍑芥暟鏄懆鏈熷嚱鏁 鍛ㄦ湡鏄2蟺 鎵浠cos2蟺=cos0=1
绛旓細鍥炵瓟锛cos2蟺 =cos(2蟺+0) =cos0 =1
绛旓細鍏蜂綋鍥炵瓟濡傚浘锛氳伪涓轰换鎰忚锛岀粓杈圭浉鍚岀殑瑙掔殑鍚屼竴涓夎鍑芥暟鐨勫肩浉绛夛細sin锛2k蟺+伪锛=sin伪 锛坘鈭圸锛cos锛2k蟺+伪锛=cos伪 锛坘鈭圸锛塼an锛2k蟺+伪锛=tan伪 锛坘鈭圸锛塩ot锛2k蟺+伪锛=cot伪锛坘鈭圸锛
绛旓細杩欐鏄2蟺搴﹁鐨勪綑寮﹀间笌0掳瑙掞紙鐩磋锛夌殑浣欏鸡鍊肩浉绛夌殑鏃跺埢銆傚洜涓0掳瑙掔殑浣欏鸡鍊煎畾涔変负1锛屾墍浠ュ綋鏃嬭浆涓鍦堝悗锛宑os2蟺鑷劧涔熺瓑浜1銆傝繖涓畝鍗曠殑閬撶悊锛岄氳繃瑙嗛涓殑娣卞叆瑙ｆ瀽锛屻cos2蟺绛変簬澶氬皯锛熷悓瀛︽病鎬濊矾锛岃佸笀甯︿綘杞绘澗瀛︼紝鏂规硶宸у鎻ず銆嬶紝甯︿綘棰嗙暐鏁板鐨勯瓍鍔涖傝繖涓湅浼煎钩鍑＄殑绛夊紡锛屽叾瀹炶暣鍚潃鍛ㄦ湡鎬у拰...
绛旓細浜屽垎涔嬒绾︾瓑浜1.5707963锛屽洜涓合绾︾瓑浜3.1415926锛岄櫎浠2灏辩害绛変簬1.5707963銆cos浜鍒嗕箣蟺绛変簬0锛宻in浜屽垎涔嬒绛変簬1銆備簩鍒嗕箣蟺鏄鍒嗘暟鍚椾簩鍒嗕箣蟺涓嶆槸鍒嗘暟锛屽垎鏁版槸涓涓暣鏁癮鍜屼竴涓鏁存暟b鐨勪笉绛変簬鏁存暟鐨勬瘮銆傁骞朵笉鏄暣鏁帮紝鑰屾槸涓涓棤闄愪笉寰幆灏忔暟锛屽睘浜庢棤鐞嗘暟锛屾墍浠ヤ簩鍒嗕箣蟺涓嶆槸鍒嗘暟銆備粈涔堟槸蟺蟺...
