1.已知函数f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4).注:π是pai.(1)求函数f(x)的最小正周期和图象的对称轴方程.(2)求函数f(x)在区间[-π/12,π/2]的值域.2.已知向量a=(cos2x,-sin2x),向量b=(根号3,-1),函数f(x
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1.已知函数f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4).注:π是pai.(1)求函数f(x)的最小正周期和图象的对称轴方程.(2)求函数f(x)在区间[-π/12,π/2]的值域.2.已知向量a=(cos2x,-sin2x),向量b=(根号3,-1),函数f(x
1.已知函数f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4).注:π是pai.
(1)求函数f(x)的最小正周期和图象的对称轴方程.
(2)求函数f(x)在区间[-π/12,π/2]的值域.
2.已知向量a=(cos2x,-sin2x),向量b=(根号3,-1),函数f(x)=向量a×向量b+m.
(1)求f(x)在[0,π]上的单调增区间.
(2)当x∈[0,π/2]时,f(x)有最小值2倍跟号3.求m
3.已知向量a=(sinx,3/2),向量b=(cosx,-1).
(1)当a‖b时,求2cos平方x-sin2x
(2)求f(x)=(a+b)×b的值域.
(麻烦尽量详细点,
1.已知函数f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4).注:π是pai.(1)求函数f(x)的最小正周期和图象的对称轴方程.(2)求函数f(x)在区间[-π/12,π/2]的值域.2.已知向量a=(cos2x,-sin2x),向量b=(根号3,-1),函数f(x
1.
已知函数f(x)=cos(2x-π/3) 2sin(x-π/4)sin(x π/4)
(1)求函数f(x)的最小正周期和图像的对称轴方程
(2)求函数f(x)在区间[-π/12,π/2]上的值域
⑴f(x)=cos(2x-π/3) 2sin(x-π/4)sin(x π/4)
=cos(2x-π/3) √2sin(x-π/4)√2sin(x π/4)
=cos(2x-π/3) (sinx-cosx)(sinx cosx)
=cos(2x-π/3) (sinx^2-cosx^2)
=cos(2x-π/3) cos2x
=1/2cos2x-√3/2sin2x cos2x
=3/2cos2x-√3/2sin2x
=√3(√3/2cos2x-1/2sin2x)
=√3sin(2x-π/3)
∴函数f(x)的最小正周期为π,图像的对称轴方程 x=kπ/2 π/6
(2)函数f(x)在区间[-π/12,π/2]上的值域 [-√3,√3]
2.
(1)函数y=T3*cos2x+sin2x+m (T为根号)
=2(T3/2*cos2x+1/2*sin2x)+m
=2[sin(2x+派/3)]+m
所以最小正周期为 2派/2=派
(2)x∈[0.3.14/2] 2x∈[0 ,派]
2x+派/3∈[派/3,4派/3]
当 2x+派/3=4派/3时 有最小值-T3+m=5
所以 m=5+T3
3.
因为向量a//向量b,得
-sinx-3/2cosx=0,得-sinx=3/2cosx
tanx=-3/2,
再化简2cos^2x-sin2x,用降幂公式得:1+cos2x=2cos^x
=1+cos2x-sin2x
再用万能公式
cos2x=(1-tan^2x)/(1+tan^x)=(1-9/4)/(1+9/4)=-5/13
sin2x=2tanx/(1+tan^x)=2*(-3/2)/(1+9/4)=-12/13,
最后将sin2x,cos2x代人,得
1-5/13+12/13=20/13