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为了得到函数y=sin3x+Cos3x的图像,可以将函数y=√2...

sin3x+cos3x=√2*(√2/2*sin3x+√2/2*cos3x)=√2cos(3x-π/4) ∴原式即求如何通过变换将y=√2cos3x的图像变成y=√2cos(3x-π/4)的图像。 而√2cos(3x-π/4)=√2cos3(x-π/12),∴观察可得将y=√2cos3x的图像向右平移π/12个单位即可得到y=√2cos3(x-π/12)=sin3x+c...

(1)向右平移π/12个单位; y=sin3x+cos3x=√2cos(3x-π/4)=√2cos3(x-π/12). 平移法则:左加右减. (2) y=√2sin(3x+π/4)=√2cos[π/2-(3x+π/4)]=√2cos[π/4-3x]=√2cos(3x-π/4) (cosx是偶函数)

这是辅助角公式

y=sin3x+cos3x =√2(√2/2sin3x+√2/2cos3x) =√2sin(3x+π/4)

sin3x+cos3x =√2 [ sin3x.cos(π/4)+cos3x.sin(π/4) ] =√2 .sin(3x+ π/4)

向右平移 π/6个单位 成为:sin(3x-π/2)

y=sin3x+cos3x =根号2 sin((3x+π/4)3x+π/4=2kπ+π/2 ,x=2kπ/3+π/12时取最大值3x+π/4=2kπ-π/2 ,x=2kπ/3+π/4时取最小值

1.f(x)=(sinx+sin3x)/(cosx+cos3x) =(sinx+3sinx-4sin^3 x)/(cosx+4cos^3 x-3cosx) =(4sinx-4sin^3 x)/(4cos^3 x-2cosx) =[4sinx(1-sin^2 x)]/[2cosx(cos^2 x-1)] =(4sinxcos^ x)/(2cosxcos2x) =(2sin2xcosx)/(2cosxcos2x) =tan2x T=π/2 2.f(x)=...

cos3x=cos(2x+x)=cos2xcosx-sin2xsinx =[(cosx)^2-(sinx)^2]cosx-2sinxcosxsinx =(cosx)^3-(sinx)^2cosx-2(sinx)^2cosx =(cosx)^3-3(sinx)^2cosx sin3x=sin(2x+x)=sin2xcosx+cos2xsinx =2sinxcosxcosx+[(cosx)^2-(sinx)^2]sinx =2sinx(cosx)^2+(...

函数 f(x)=2sin(3x- 3π 4 ) =2sin(3x- π 4 - π 2 )=-2cos(3x- π 4 ),故①不正确.函数 f(x)=2sin(3x- 3π 4 ) ,T= 2π w = 2π 3 ,故最小正周期是 2π 3 ,故②正确.函数 f(x)=2sin(3x- 3π 4 ) 的单调增区间为2kπ- π 2 ≤3x- π 4 ≤2kπ+ π 2 ,...

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