Question

三角函数转化问题，求详细过程

请问这两个公式如何推算而来？

Answer 1

1. sin(3t) = sin(2t+t) 
   

   = sin(2t)cost + cos(2t)sint

   = (2sintcost)cost + (cos²t - sin²t)sint

   = 2sintcos²t + sintcos²t - sin³t

   = 3sintcos²t - sin³t

   = 3sint(1-sin²t) - sin³t

   = 3sint - 3sin³t - sin³t

   = 3sint - 4sin³t

2. cos(3t) = cos(2t+t)

   = cos(2t)cost - sin(2t)sint

   = (2cos²t - 1)cost - (2sintcost)sint

   = 2cos³t - cost - 2sin²tcost

   = 2cos³t - cost - 2(1-cos²t)cost

   = 2cos³t - cost - 2cost + 2cos³t

   = 4cos³t - 3cost

注：公式中共用到几个公式：

1. sin²α + cos²α = 1

2. cos(2α)=cos²α-sin²α = 2cos²α-1

3. sin(2α) = 2sinαcosα

4. sin(α+β) = sinαcosβ+cosαsinβ

5. cos(α+β) = cosαcosβ - sinαsinβ

Answer 2

异名三角函数平移，先通过诱导公式将异名转化为同名，在平移。如2cos(π+x)=2cos [π/2+(π/2+x) ]= -2sinπ/2,再平移

Answer 3

不会哦，亲，对不起

Answer 4

异名三角函数平移，先通过诱导公式将异名转化为同名，在平移。如2cos(π+x)=2cos [π/2+(π/2+x) ]= -2sinπ/2,再平移