已知函数y1=3sin(2x-π/3),y2=4sin（2x+π/3,那么函数y=y1+y2的振幅A的值是多少?

Question

已知函数y1 =3sin(2x-π/3),y2 =4sin（2x+π/3,那么函数y=y1+y2的振幅A的值是多少?

Answer 1

确定题目没打错吗?~
你看是这样不?
已知函数y1=3sin(2x-3/Л),y2=4sin(2x+3/Л),求函数y=y1+y2的振幅.
已知函数y1=3sin(2x-3/Л),y2=4sin(2x+3/Л), y1=3[sin2x/Лcos3/Л-cos2x/Лsin3/Л];
y2=4[sin2x/Лcos3/Л+cos2x/Лsin3/Л];
y=y1+y2=7sin2x/Лcos3/Л+cos2x/Лsin3/Л
=(7cos3/Л)sin2x/Л+(sin3/Л)cos2x/Л
知道：asinx+bcosx形的振幅A＝√a^2+b^2,所以上题就是√(7cos3/Л)^2+(sin3/Л)^2=
√48(cos3/Л )^2+1