为什么|cosx|≤1 为什么 存在x∈R,cosx≤-1 是对的
cosX\u7684\u53d6\u503c\u8303\u56f4\u4e3a\u4ec0\u4e48\u662f-1\u2264cosX\u22641\u521d\u4e2d\u7684\u65f6\u5019\uff0c\u662f\u5728\u76f4\u89d2\u4e09\u89d2\u5f62\u4e2d\u7ed9\u7684cosX\u7684\u5b9a\u4e49\uff0c\u662f\u6307\u89d2X\u7684\u90bb\u8fb9/\u659c\u8fb9\u3002\u56e0\u4e3a\u659c\u8fb9\u6700\u957f\uff0c \u6240\u4ee5\u6bd4\u503c\u80af\u5b9a\u5c0f\u4e8e1\uff0c\u81f3\u4e8e\u5927\u4e8e-1\uff0c\u662f\u56e0\u4e3a\u5230\u4e86\u9ad8\u4e2d\u9636\u6bb5\uff0c\u6982\u5ff5\u8fdb\u884c\u4e86\u63a8\u5e7f\uff0c\u4f46\u5b9e\u9645\u4e0a\u51e0\u4f55\u610f\u4e49\u5dee\u4e0d\u591a\uff0c\u591a\u4e86\u65b9\u5411\uff0c\u4f53\u73b0\u5728\u6bd4\u503c\u4e2d\u5c31\u662f\u591a\u4e86\u8d1f\u53f7\uff0c\u8303\u56f4\u56e0\u6b64\u5728\uff08-1,1\uff09\u4e4b\u95f4\u3002
\u5f53-1<cosX<1\u65f6\uff0c-1<-cosX<1\uff0c\u6240\u4ee5\u518d\u52a01,\u67090<-cosX+1<2,\u5373\u4e3a0<1-cosX<2.
\u7b49\u53f7\u7684\u5730\u65b9\u5c5e\u4e8e\u5bb9\u6613\u7406\u89e3\u7684\u4e2a\u522b\u60c5\u51b5\uff0c\u5c31\u4e0d\u52a0\u4e0a\u53bb\u4e86
\u5177\u4f53\u9898\u76ee\uff1f
因为sin²x+cos²x=1所以cos²x=1-sin²x
而sin²x≥0
所以以cos²x=1-sin²x≤1
所以|cosx|≤1
绛旓細鍥犱负sin²x+cos²x=1 鎵浠os²x=1-sin²x 鑰宻in²x鈮0 鎵浠ヤ互cos²x=1-sin²x鈮1 鎵浠|cosx|鈮1
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绛旓細姝ｄ綑寮︿笉绠″灏戝害锛屽奸兘鍦ㄦ璐涓涔嬮棿锛宑os=涓磋竟/鏂滆竟=x/r,鑰屽湪鐩磋涓夎褰腑锛屼复杈规案杩滃皬浜庢枩杈癸紝鍙湁褰0搴︽垨180搴︾殑鏃跺欙紝涓磋竟鍜屾枩杈归噸鍚堬紝姣斿间负卤1
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绛旓細-蟺/6<x<0鏄鍑芥暟 0x<蟺/3鏄噺鍑芥暟 鎵浠=0锛宑osx鏈澶=cosx=1 鏈灏忓湪杈圭晫 cos(-蟺/6)=鈭3/2 cos(蟺/3)=1/2 x鍙栦笉鍒跋/3 鎵浠ュ簲璇ユ槸1/2<cosx鈮1
