已知函数f(x)=sin²x+2sinxcosx+3cos²x,x∈R已知函数f(x)=sin²x+2sinxcosx+3cos²x,x∈RR,求:(1)函数f(x)的最小正周期、最大值(2)函数f(x)的单调增区间.
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![已知函数f(x)=sin²x+2sinxcosx+3cos²x,x∈R已知函数f(x)=sin²x+2sinxcosx+3cos²x,x∈RR,求:(1)函数f(x)的最小正周期、最大值(2)函数f(x)的单调增区间.](/uploads/image/z/1618342-70-2.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3Dsin%26%23178%3Bx%2B2sinxcosx%2B3cos%26%23178%3Bx%2Cx%E2%88%88R%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3Dsin%26%23178%3Bx%2B2sinxcosx%2B3cos%26%23178%3Bx%2Cx%E2%88%88RR%2C%E6%B1%82%EF%BC%9A%EF%BC%881%EF%BC%89%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%E7%9A%84%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F%E3%80%81%E6%9C%80%E5%A4%A7%E5%80%BC%EF%BC%882%EF%BC%89%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%E7%9A%84%E5%8D%95%E8%B0%83%E5%A2%9E%E5%8C%BA%E9%97%B4%EF%BC%8E)
已知函数f(x)=sin²x+2sinxcosx+3cos²x,x∈R已知函数f(x)=sin²x+2sinxcosx+3cos²x,x∈RR,求:(1)函数f(x)的最小正周期、最大值(2)函数f(x)的单调增区间.
已知函数f(x)=sin²x+2sinxcosx+3cos²x,x∈R
已知函数f(x)=sin²x+2sinxcosx+3cos²x,x∈RR,求:
(1)函数f(x)的最小正周期、最大值
(2)函数f(x)的单调增区间.
已知函数f(x)=sin²x+2sinxcosx+3cos²x,x∈R已知函数f(x)=sin²x+2sinxcosx+3cos²x,x∈RR,求:(1)函数f(x)的最小正周期、最大值(2)函数f(x)的单调增区间.
f(x)=1+2cos^2x+sin2x
=(cos2x+2)+sin2x
=(cos2x+sin2x)+2
=√2sin(2x+π/4)+2
(1)函数f(x)的最小正周期为π、最大值为√2+2;
(2)2kπ-π/2
fx=1-2sinx^2+sin2x=cos2x+sin2x=根号2sin(2x+45)+2
1.t=pai,最大值2+根号2
2.2x+45在(-π/2+2kπ,π/2+2kπ)解处即可
f(x)=sin²x+2sinxcosx+3cos²x
=sin2x+2cos²x+1
=sin2x+cos2x+2
=√2sin(2x+π/4)+2
(1) 最小正周期=2π/2=π
f(x)最大=2+√2
(2) 单增区间2x+π/4∈[2kπ-π/2, 2kπ+π/2]
x∈[kπ-3π/8, kπ+π/8] k∈Z
希望能帮到你O(∩_∩)O