f(x)=sinx/2cosx/2+1/2sin(x+π/2)单调区间是什么

f(x)=sinx/2cosx/2+1/2sin(x+π/2)单调区间是什么
f(x)=sinx/2cosx/2+1/2sin(x+π/2)单调区间是什么

f(x)=sinx/2cosx/2+1/2sin(x+π/2)单调区间是什么
f(x)=sinx/2cosx/2+1/2sin(x+π/2)
=1/2sinx+1/2cosx
=√2/2 （ √2/2sinx+√2/2cosx）
=√2/2 （sinxcosπ/4+sinπ/4cosx）
=√2/2 sin(x+π/4)
1.
2kπ-π/2

函数f(x)=sin(x/2)cos(x/2)+cos²(x/2)
=(sin(x/2)+cos(x/2))cos(x/2)
=√2(√2/2sin (x/2)+√2/2cos(x/2))cos(x/2)
=√2(sin (x/2) cosπ/4+cos (x/2) sinπ/4)cos(x/2)
=√2sin(x/2+π/4)cos(x/2)
=...

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函数f(x)=sin(x/2)cos(x/2)+cos²(x/2)
=(sin(x/2)+cos(x/2))cos(x/2)
=√2(√2/2sin (x/2)+√2/2cos(x/2))cos(x/2)
=√2(sin (x/2) cosπ/4+cos (x/2) sinπ/4)cos(x/2)
=√2sin(x/2+π/4)cos(x/2)
=√2/2sin(x+π/4)+ 1/2
1、
f(x) = √2/2sin(x+π/4)+ 1/2
sin(x),cos(x)的定义域为R,值域为〔-1,1〕
即： -π/2+2kπ≤x+π/4≤π/2+2kπ
函数f(x)的单增区间为-3π/4+2kπ≤x≤π/4+2kπ.(k∈z).
即：【-3π/4+2kπ，π/4+2kπ】

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f(x)=(1/2)sinx+(1/2)cosx
=(√2/2)[sinx*(√2/2)+cosx*(√2/2)]
=(√2/2)*[sinx*cos(π/4)+cosx*sin(π/4)]
=(√2/2)sin(x+π/4)
增区间
2kπ-π/2≤x+π/4≤2kπ+π/2
即 ...

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f(x)=(1/2)sinx+(1/2)cosx
=(√2/2)[sinx*(√2/2)+cosx*(√2/2)]
=(√2/2)*[sinx*cos(π/4)+cosx*sin(π/4)]
=(√2/2)sin(x+π/4)
增区间
2kπ-π/2≤x+π/4≤2kπ+π/2
即 2kπ-3π/4≤x≤2kπ+π/4
所以，增区间为 【 2kπ-3π/4，2kπ+π/4】，k∈Z
减区间
2kπ+π/2≤x+π/4≤2kπ+3π/2
即 2kπ+π/4≤x≤2kπ+5π/4
所以，减区间为 【 2kπ+π/4，2kπ+5π/4】，k∈Z

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单调增区间为[-兀/4+2k兀,3兀/4+2k兀]

f(x)=sinx/2cosx/2+1/2sin(x+π/2)
=1/2sinx+1/2cosx
=（根号2）/2*sin(x+π/4)


增区间
2kπ-π/2≤x+π/4≤2kπ+π/2
即 2kπ-3π/4≤x≤2kπ+π/4
所以，增区间为 【 2kπ-3π/4，2kπ+π/4】，k∈Z

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f(x)=sinx/2cosx/2+1/2sin(x+π/2)
=1/2sinx+1/2cosx
=（根号2）/2*sin(x+π/4)


增区间
2kπ-π/2≤x+π/4≤2kπ+π/2
即 2kπ-3π/4≤x≤2kπ+π/4
所以，增区间为 【 2kπ-3π/4，2kπ+π/4】，k∈Z




减区间
2kπ+π/2≤x+π/4≤2kπ+3π/2
即 2kπ+π/4≤x≤2kπ+5π/4
所以，减区间为 【 2kπ+π/4，2kπ+5π/4】，k∈Z




化简过程用到的公式

1、sin2x=2sinx cosx
2、sin(x+π/2)=(根号2)/2*(sinx+cosx)
3、sin(x+π/2)=cosx



y=log2（f（X）*h（X））=
log2(（根号2）/2*sin(x+π/4)*cos（x+5π/4))
=1/2+log2(-sin(x+π/4)*cos（x+π/4))
=1/2+log2(-1/2sin(2x+π/2))
=-1/2+log2(-cos(2x))


当cos（2x）=-1时 取最大值

x=2kπ+π

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