若F(X)=ASIN(X+PI/4)+3SIN(X—PI/4)是偶函数,则A=
问题描述:
若F(X)=ASIN(X+PI/4)+3SIN(X—PI/4)是偶函数,则A=
答
∵f(x)=Asin(x+π/4)+3sin(x-π/4)是偶函数∴f(-x)=f(x)即Asin(-x+π/4)+3sin(-x-π/4)=Asin(x+π/4)+3sin(x-π/4)A[sin(-x+π/4)-sin(x+π/4)]=3[sin(x-π/4)-sin(-x-π/4)]2Acosπ/4sin(-x)=6cos(-π/4)sinx-2Acos...