求一道函数体: (1)求函数y=3cos(2x-π/3),x∈R的单调区间; (2)求函数y=sin(-3x+π/4),x∈R的单调区间.求详细过程~谢谢啦、
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![求一道函数体: (1)求函数y=3cos(2x-π/3),x∈R的单调区间; (2)求函数y=sin(-3x+π/4),x∈R的单调区间.求详细过程~谢谢啦、](/uploads/image/z/3012015-39-5.jpg?t=%E6%B1%82%E4%B8%80%E9%81%93%E5%87%BD%E6%95%B0%E4%BD%93%3A+%281%29%E6%B1%82%E5%87%BD%E6%95%B0y%3D3cos%282x-%CF%80%2F3%29%2Cx%E2%88%88R%E7%9A%84%E5%8D%95%E8%B0%83%E5%8C%BA%E9%97%B4%3B+%282%29%E6%B1%82%E5%87%BD%E6%95%B0y%3Dsin%28-3x%2B%CF%80%2F4%29%2Cx%E2%88%88R%E7%9A%84%E5%8D%95%E8%B0%83%E5%8C%BA%E9%97%B4.%E6%B1%82%E8%AF%A6%E7%BB%86%E8%BF%87%E7%A8%8B%7E%E8%B0%A2%E8%B0%A2%E5%95%A6%E3%80%81)
求一道函数体: (1)求函数y=3cos(2x-π/3),x∈R的单调区间; (2)求函数y=sin(-3x+π/4),x∈R的单调区间.求详细过程~谢谢啦、
求一道函数体: (1)求函数y=3cos(2x-π/3),x∈R的单调区间; (2)求函数y=sin(-3x+π/4),x∈R的单调区间.
求详细过程~
谢谢啦、
求一道函数体: (1)求函数y=3cos(2x-π/3),x∈R的单调区间; (2)求函数y=sin(-3x+π/4),x∈R的单调区间.求详细过程~谢谢啦、
1. y=cosx 单调减区间为 [2kπ,2kπ+π]
函数y=3cos(2x-π/3),x∈R的单调区间
2kπ<=2x-π/3<=2kπ+π 解得
单调减区间 【kπ+π/6,kπ+2π/3】
y=cosx 单调增减区间为 [2kπ-π,2kπ]
函数y=3cos(2x-π/3),x∈R的单调增区间
2kπ-π<=2x-π/3<=2kπ 解得
单调增区间 【kπ-2π/3,kπ+π/6】
2. y=sinx 单调增区间为 [2kπ-π/2,2kπ+π/2]
函数y=sin(-3x+π/4)=-sin(3x-π/4)
函数y=sin(-3x+π/4)=-sin(3x-π/4) 单调减区间为
2kπ-π/2<=3x-π/4<=2kπ+π/2
单调减区间为 【2kπ/3-π/12,2kπ/3+3π/12】
y=sinx 单调减区间为 [2kπ+π/2,2kπ+3π/2]
函数y=sin(-3x+π/4)=-sin(3x-π/4) 单调增区间为
2kπ+π/2<=3x-π/4<=2kπ+3π/2
单调增区间为 【2kπ/3+3π/12,2kπ/3+7π/12】
πππ
(1)递增区间:令 -π+2kπ <=2x-π/3<= 0+2kπ k=0,1,2,3.......
递减区间:令 0+2kπ <=2x-π/3<= π+2kπ k=0,1,2,3.......
(2)递增区间:令 -π/2+2kπ <=-3x+π/4<= π/2+2kπ k=0,1,2,3.......
递减...
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(1)递增区间:令 -π+2kπ <=2x-π/3<= 0+2kπ k=0,1,2,3.......
递减区间:令 0+2kπ <=2x-π/3<= π+2kπ k=0,1,2,3.......
(2)递增区间:令 -π/2+2kπ <=-3x+π/4<= π/2+2kπ k=0,1,2,3.......
递减区间:令 π/2+2kπ <=(-3x+π/4<= 3π/2+2kπ k=0,1,2,3.......
求出x的范围即可
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