作业帮一.求下列函数的值域:(1)y=sinx+√3cosx (|x|≤π/2) (2)y=cos²x+sinx+1 (|x|≦π/3) (3)y=sin²x+2sinxcosx+3cos²x+1二.已知函数f(x)=2sin(π-x)cosx(1)求f(x)的最小正周期 (2)求f(x)在区间[-π/6,π/2]上的最大值和
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![一.求下列函数的值域:(1)y=sinx+√3cosx (|x|≤π/2) (2)y=cos²x+sinx+1 (|x|≦π/3) (3)y=sin²x+2sinxcosx+3cos²x+1二.已知函数f(x)=2sin(π-x)cosx(1)求f(x)的最小正周期 (2)求f(x)在区间[-π/6,π/2]上的最大值和](/uploads/image/z/5346998-62-8.jpg?t=%E4%B8%80.%E6%B1%82%E4%B8%8B%E5%88%97%E5%87%BD%E6%95%B0%E7%9A%84%E5%80%BC%E5%9F%9F%3A%281%29y%3Dsinx%2B%E2%88%9A3cosx+%28%7Cx%7C%E2%89%A4%CF%80%2F2%29+%282%29y%3Dcos%26%23178%3Bx%2Bsinx%2B1+%28%7Cx%7C%E2%89%A6%CF%80%2F3%29+%283%29y%3Dsin%26%23178%3Bx%2B2sinxcosx%2B3cos%26%23178%3Bx%2B1%E4%BA%8C.%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3D2sin%28%CF%80-x%29cosx%281%29%E6%B1%82f%28x%29%E7%9A%84%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F+%282%29%E6%B1%82f%28x%29%E5%9C%A8%E5%8C%BA%E9%97%B4%5B-%CF%80%2F6%2C%CF%80%2F2%5D%E4%B8%8A%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC%E5%92%8C)
一.求下列函数的值域:(1)y=sinx+√3cosx (|x|≤π/2) (2)y=cos²x+sinx+1 (|x|≦π/3) (3)y=sin²x+2sinxcosx+3cos²x+1二.已知函数f(x)=2sin(π-x)cosx(1)求f(x)的最小正周期 (2)求f(x)在区间[-π/6,π/2]上的最大值和
一.求下列函数的值域:(1)y=sinx+√3cosx (|x|≤π/2) (2)y=cos²x+sinx+1 (|x|≦π/3) (3)y=sin²x+2sinxcosx+3cos²x+1
二.已知函数f(x)=2sin(π-x)cosx
(1)求f(x)的最小正周期 (2)求f(x)在区间[-π/6,π/2]上的最大值和最小值
三.求下列函数的单调区间:
(1)y=cos2x (2)y=sin(π/4-3x) (3)f(x)=sinx(sinx-cosx)
一.求下列函数的值域:(1)y=sinx+√3cosx (|x|≤π/2) (2)y=cos²x+sinx+1 (|x|≦π/3) (3)y=sin²x+2sinxcosx+3cos²x+1二.已知函数f(x)=2sin(π-x)cosx(1)求f(x)的最小正周期 (2)求f(x)在区间[-π/6,π/2]上的最大值和
一1、y=1/2sin(x+π/3)
令t=x+π/3 y=sint/2 t∈[-π/6,5π/6] y∈[-1/4,1/2]
2、y=-t^2+t+2 t=sinx∈[-根3/2,根3/2]
y∈[5/4-根3/2,9/4]
3、y=2(t^2+t+2)/(1+t^2) t=tanx
使用△法 y∈[3-根2,3+根2]
二1、f(x)=sin(2x) T=π f=sint t∈[-π/3,π] f∈[-根3/2,1]
三3、f(x)=sinx(根2sin(x-π/4))=根2/2(根2/2+sin(2x-3π/4))
（1）【-1 2】（2）【5/4-根号3/2 9/4】（3）【-根号2 根号2】
（1）π （2）f（x）min=1 f（x）max=2