若f(x)=asin(x+π/4)+3sin(x-π/4)是偶函数,则实数a的值为
来源:百度知道 编辑:UC知道 时间:2024/06/15 03:09:31
要有过程
f(-x)=asin(-x+π/4)+3sin(-x-π/4)
=-asin(x-π/4)-3sin(x+π/4)
f(x)=asin(x+π/4)+3sin(x-π/4)是偶函数
所以f(x)=f(-x)
所以asin(x+π/4)+3sin(x-π/4)=-asin(x-π/4)-3sin(x+π/4)
对应系数相等
明显a=-3
f(x)=asin(x+π/4)+3sin(x-π/4)=a(sinxcosπ/4+cosxsinπ/4)+3(sinxcosπ/4-cosxsinπ/4)=sinx(a+3)(根号2)/2+cosx(a-3)(根号2)/2
f(-x)=sin(-x)(a+3)(根号2)/2+cos(-x)(a-3)(根号2)/2
=-sinx(a+3)(根号2)/2+cosx(a-3)(根号2)/2 f(x)偶函数
=f(x)=sinx(a+3)(根号2)/2+cosx(a-3)(根号2)/2
2sinx(a+3)(根号2)/2=0 所以a=-3
若f(x)=asinx+cosx的图象关于直线x=π/8成轴对称图形,则g(x)=asin(a+1)x的最小正周期是___
已知f(x)=asin x-bcos x(a,b为常数,a≠0,x∈R)
已知函数f(x)=Asin(2x+q)(A>0),且对任意的实数X满足
f(x+π)=f(-x),且f(-x)=f(x),那么f(x)可以是( )
f(x)=[x[x]],[x]表
若函数f(x)=1/1+x时f(x+h)-f(x)=?
已知函数 f(x)=Asin(wx+q)(A>0,w>0 )的图象.....
若f(x)满足关系式f(x)+2f(1/x)=3x,则f(x)
已知f[f(x)]=f(x)
f(x)=f(x+2)且f(-x)=-f(x);若f(x)在(-3,-2)区界递减,且f(x)>0,