已知函数f(x)=sin(x-派/3)+√3cos(x-派/3)
1.求f(x)在[0.2派]上的单调递增区间2.设函数g(x)=(1+sinx)f(x)求g(x)值域...
1.求f(x)在[0.2派]上的单调递增区间 2.设函数g(x)=(1+sinx)f(x) 求g(x)值域
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f(x)=sin(x-派/3)+√3cos(x-派/3)
=2[1/2*sin(x-π/3)+√3/2*cos(x-π/3)]
=2sin(x-π/3+π/3)
=2sinx
f(x)在[0.2派]上的单调递增区间为
[0,π/2] ,[3π/2,2π]
2
g(x)=(1+sinx)sinx
=sin²x+sinx
=(sinx+1/2)²-1/4
当sinx=-1/2时，f(x)min=-1/4
当sinx=1时，f(x0max=2
g(x)值域为[-1/4.2]
f(x)=sin(x-派/3)+√3cos(x-派/3)
=2[1/2*sin(x-π/3)+√3/2*cos(x-π/3)]
=2sin(x-π/3+π/3)
=2sinx
f(x)在[0.2派]上的单调递增区间为
[0,π/2] ,[3π/2,2π]
2
g(x)=(1+sinx)sinx
=sin²x+sinx
=(sinx+1/2)²-1/4
当sinx=-1/2时，f(x)min=-1/4
当sinx=1时，f(x0max=2
g(x)值域为[-1/4.2]
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