求函数fx=sin(2x-π/4)-2根号2sin²x的单调递减区间及对称轴
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![求函数fx=sin(2x-π/4)-2根号2sin²x的单调递减区间及对称轴](/uploads/image/z/699796-28-6.jpg?t=%E6%B1%82%E5%87%BD%E6%95%B0fx%3Dsin%282x-%CF%80%2F4%29-2%E6%A0%B9%E5%8F%B72sin%26%23178%3Bx%E7%9A%84%E5%8D%95%E8%B0%83%E9%80%92%E5%87%8F%E5%8C%BA%E9%97%B4%E5%8F%8A%E5%AF%B9%E7%A7%B0%E8%BD%B4)
求函数fx=sin(2x-π/4)-2根号2sin²x的单调递减区间及对称轴
求函数fx=sin(2x-π/4)-2根号2sin²x的单调递减区间及对称轴
求函数fx=sin(2x-π/4)-2根号2sin²x的单调递减区间及对称轴
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你好
f(x)=sin(2x-π/4)-2√2sin²x
=sin2xcosπ/4-cos2xsinπ/4-√2(1-cos2x)
=√2/2 sin2x- √2/2 cos2x +√2cos2x-√2
=√2/2 sin2x+√2/2 cos2x-√2
=sin(2x+π/4)-√2
函数f(x)=sinx的对称区间是
[2Kπ-...
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你好
f(x)=sin(2x-π/4)-2√2sin²x
=sin2xcosπ/4-cos2xsinπ/4-√2(1-cos2x)
=√2/2 sin2x- √2/2 cos2x +√2cos2x-√2
=√2/2 sin2x+√2/2 cos2x-√2
=sin(2x+π/4)-√2
函数f(x)=sinx的对称区间是
[2Kπ-π/2,2Kπ+π/2]单调递增
[2Kπ+π/2,2Kπ+3π/2]单调递减
对称轴是Kπ+π/2
所以
2Kπ-π/2≤2x+π/4≤2Kπ+π/2
解得Kπ-3π/8≤x≤Kπ+π/8时,函数单调递增
2Kπ+π/2≤2x+π/4≤2Kπ+3π/2
解得Kπ+π/8≤x≤Kπ+5π/8时,函数单调递减
2x+π/4=Kπ+π/2
对称轴为x=Kπ/2+π/8
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