试用sinx表示sin3x

蔡先高4203比较sin1,sin2与sin3的大小关系为___. -
奚宽利18712915630 ______[答案] ∵1弧度≈57°,2弧度≈114°,3弧度≈171°.∴sin1≈sin57°,sin2≈sin114°=sin66°.sin3≈171°=sin9°∵y=sinx在(0,90°)上是增函数,∴sin9°

蔡先高4203化简sin(3π - x) -
奚宽利18712915630 ______ sin(3n-x)=sin(n-x)=sinx

蔡先高4203试用sinα表示3sinα -
奚宽利18712915630 ______ 解:sin3α=3sinα-4sin³α 推导过程 sin3α=sin(2α+α)=sin2αcosα+cos2αsinα=2sinαcos²α+(1-2sin²α)sinα=2sinα(1-sin²α)+sinα-2sin³α=3sinα-4sin³α

蔡先高4203试用sinθ表示sin3θ -
奚宽利18712915630 ______[答案] sin3θ =sin(2θ+θ) =sin2θcosθ+cos2θsinθ =2sinθcosθcosθ+(1-2(sinθ)^2)sinθ =2sinθ(1-(sinθ)^2)+(1-2(sinθ)^2)sinθ =2sinθ-2(sinθ)^3+sinθ-2(sinθ)^3 =3sinθ-4(sinθ)^3

蔡先高4203用sinα表示sin3α 用cosβ表示cos3β -
奚宽利18712915630 ______ sin3a=sin(2a+a)=sin2acosa+cos2asina=2sinacos^2a+cos^2asina-sin^3a=3sinacos^2a-sin^3a=3sina(1-sin^2a)-sin^3a=3sina-4sin^3a cos3a=cos(2b+b)=cos2bcosb-sin2bsinb=cos^3b-cosbsin^2b-2sin^2bcosb=cos^3b-3cosbsin^2b=cos^3b-3cosb(1-cos^2b)=4cos^3b-3cosb

蔡先高4203求证sin3xsin^x+cos3cos^3x=cos^3(2x) -
奚宽利18712915630 ______ (sin^3x表示sinx的三次方) sin3xsin^3x+cos3xcos^3x=cos^3(2x) 证明:左侧=sin(x+2x)sin^3x+cos(x+2x)cos^3x =sin^4xcos2x+sin2xcosxsin^3x+cos^4xcos2x-sinxcos^3xsin2x =sin^4xcos2x+2sin^4xcos^2x+cos^4xcos2x-2sin^2xcos^4x =cos2x(sin^4x...

蔡先高4203试用sinα表示3sinα手抖发错了是试用sinα表示sin3α -
奚宽利18712915630 ______[答案] 解:sin3α=3sinα-4sin³α推导过程sin3α=sin(2α+α)=sin2αcosα+cos2αsinα=2sinαcos²α+(1-2sin²α)sinα=2sinα(1-sin²α)+sinα-2sin³α=3sinα-4sin³α

蔡先高4203sin3xcos4x=1/2(sin7x - sinx)公式是什么? -
奚宽利18712915630 ______[答案] sin(x+y)=sinXcosY+cosXsinYsin(x-y)=sinXcosY-cosXsinYsin(7x)=sin(3x+4x)2sin3xcos4x=sin7x-sinx2sin3xcos4x=sin(3x+4x)-sinx2sin3xcos4x=sin3xcos4x + cos3xsin4x - sinxsin3xcos4x- cos3xsin4x= -sinxsin(3x-4x)...

蔡先高4203解方程 sinxsin7x=sin3xsin5x -
奚宽利18712915630 ______[答案] cos(8x)=cos(x+7x)=cosxcos7x-sinxsin7x cos(8x)=cos(3x+5x)=cos3xcos5x-sin3xsin5x sinxsin7x=sin3xsin5x cosxcos7x=cos3xcos5x cosxcos7x+sinxsin7x=cos3xcos5x+sin3xsin5x cos(6x)=cos(x) 根据图像得: (1) 6x=x+(k*360) x=72k(k属于自然数) ...

蔡先高4203函数y=3sin(二分之一x减四分之派)此函数图像是由y=sinx经过怎样的变化得到的? -
奚宽利18712915630 ______[答案] y=3sin(x/2-π/4), 先把y=sinx向右移动π/4单位得到y=sin(x-π/4); 再把x坐标延长至原来的2倍,得到y=sin(x/2-π/4); 最后把y坐标延长至原来的3倍,得到y=3sin(x/2-π/4).