Question

余弦波计算Acos（wt + u) +Bcos(wt + z)请问如何化简.

Answer 1

Acos（wt + u) +Bcos(wt + z)

=A(coswtcosu-sinwtsinu)+B(coswtcosz-sinwtsinz)

=(Acosu+Bcosz)coswt-(Asinu+Bsinz)sinwt

=(1/((Acosu+Bcosz)^2+(Asinu+Bsinz)^2)^(1/2)cos(wt+m)

=Ccos(wt+m)

即为所求

其中C=(1/((Acosu+Bcosz)^2+(Asinu+Bsinz)^2)^(1/2)

=(A^2+B^2+2ABcos(u-z))^(1/2)

cosm=(Acosu+Bcosz)/C,sinm=(Asinu+Bsinz)/C