cosx<1/2,然后怎么求x的取值范围 cos x>=1/2..求x取值范围

cosx\uff1c=1/2\uff0c\u6c42x\u7684\u53d6\u503c\u8303\u56f4


\u5206\u6790\uff1a

\u9996\u5148\u8981\u4e86\u89e3\u4f59\u5f26\u51fd\u6570\u7684\u56fe\u76f8
\u5728\u5750\u6807\u7cfb\u4e2d\u4f59\u5f26\u56fe\u50cf\u8fc7
.....\u3001(-\u03c0\uff0c-1)\\uff08-\u03c0/2,0\uff09\u3001\uff080\uff0c1\uff09\u3001\uff08\u03c0/2\uff0c0\uff09\u3001\uff08\u03c0\uff0c-1\uff09\u3001...
\u81ea\u5df1\u753b\u51fa\u4f59\u5f26\u56fe\u76f8

\u518d\u5728\u5750\u6807\u7cfb\u4e2d\u753b\u51fa\u76f4\u7ebfy=1/2\uff0c\u4e0e\u521a\u624d\u753b\u7684\u4f59\u5f26\u56fe\u76f8\u6709\u597d\u591a\u4ea4\u70b9\u3002\u90a3\u4e48\uff0c\u76f4\u7ebf\u5c06\u4f59\u5f26\u56fe\u50cf\u5206\u5272\u6210\u4e86n\u591a\u5355\u5143\u3002\u6709\u5728\u76f4\u7ebf\u4e0a\u9762\u7684\u4e5f\u6709\u5728\u76f4\u7ebf\u4e0b\u9762\u7684\uff0c\u5728\u76f4\u7ebf\u4e0a\u9762\u7684\u5c31\u662fcos x>=1/2\u7684\u90e8\u5206\uff0c\u6240\u6709\u76f4\u7ebf\u4e0a\u9762\u7684\u66f2\u7ebf\u5728x\u8f74\u4e0a\u7684\u6295\u5f71\u5bf9\u5e94\u7684x\u533a\u57df\u5c31\u662fx\u7684\u53d6\u503c\u8303\u56f4\u3002


\u6c42\u89e3\uff1a

\u5728\uff08-\u03c0\uff0c\u03c0\uff09\u533a\u95f4\u5185
\u5f53cos =1/2\u65f6 x=\u03c0/3\u6216x=-\u03c0/3(\u53ef\u5728\u4e09\u89d2\u51fd\u6570\u8868\u4e2d\u67e5\u51fa\uff09
\u5219\u5728\u8fd9\u4e2a\u533a\u95f4\u5185cos x>=1/2\u7684x\u53d6\u503c\u8303\u56f4\u5c31\u662f -\u03c0/3<=x<=\u03c0/3

\u5219\u5728\u6574\u4e2a\u5750\u6807\u8f74\u4e0a\uff1a
\u5f53cos >=1/2\u65f6 x\u53d6\u503c\u8303\u56f4\u5c31\u662f -\u03c0/3+2k\u03c0<=x<=\u03c0/3=2k\u03c0 (k=\u6574\u6570)


\u8fd9\u9053\u9898\u6ca1\u6709\u7ed9\u51fa\u5b9a\u4e49\u57df\u5c31\u53ea\u80fd\u662f\u8fd9\u4e2a\u7b54\u6848\u4e86\uff0c\u5982\u679c\u6709\u5b9a\u4e49\u57df\u5c31\u5728\u5b9a\u4e49\u57df\u5185\u6c42\u89e3\u5c31\u53ef\u4ee5\u4e86

\u90fd\u597d\u51e0\u5e74\u6ca1\u5b66\u6570\u5b66\u4e86\uff0c\u52c9\u5f3a\u60f3\u8d77\u6765\u7684\uff0c\u5e0c\u671b\u5bf9\u4f60\u6709\u5e2e\u52a9\u3002

cosx=1/2 则x=2kπ+π/3或2kπ+2π/3 

如图 

所以2kπ+π/3<x<2kπ+5π/3



你可以画出Y=COSX的函数图,然后再在Y轴上当Y=1/2时做一条垂直于Y轴Y=1/2的直线,低于这条直线的部分,,可以看到当 60度--300度时满足条件(不包括60,300,可转化为多少派) 然后在 60+360*N<X<300+360*N N取全体正负整数和0

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