f(x)=asin(x+π/4)+bsin(x-π/4) (ab不为0)是偶函数,有序实数对(a,b)可以是?
来源:学生作业帮助网 编辑:作业帮 时间:2024/04/29 10:02:03
f(x)=asin(x+π/4)+bsin(x-π/4) (ab不为0)是偶函数,有序实数对(a,b)可以是?
f(x)=f(-x)
f(x)=asin(x+π/4)+bsin(x-π/4)
f(-x)=asin(-x+π/4)+bsin(-x-π/4)
=-bsin(x+π/4)-asin(x-π/4)
所以a=-b
我认为只要满足a=-b的都可以
f(x)=a[sinxcosπ/4+cosxsinπ/4]+b[sinxcosπ/4-cosxsinπ/4]
=√2a/2[sinx+cosx]+√2b/2[sinx-cosx]
f(-x)=√2a/2[sin(-x)+cos(-x)]+√2b/2[sin(-x)-cos(-x)]
=√2a/2[-sinx+cosx]+√2b/2[-sinx-...
全部展开
f(x)=a[sinxcosπ/4+cosxsinπ/4]+b[sinxcosπ/4-cosxsinπ/4]
=√2a/2[sinx+cosx]+√2b/2[sinx-cosx]
f(-x)=√2a/2[sin(-x)+cos(-x)]+√2b/2[sin(-x)-cos(-x)]
=√2a/2[-sinx+cosx]+√2b/2[-sinx-cosx]
=√2a/2[-sinx+cosx]-√2b/2[sinx+cosx]
=f(x)
比较系数得:
√2a/2=-√2b/2
a=-b
收起
f(x)=asin(x+π/4)+3sin(x-π/4)是偶函数,求a.
f(x)=asin(πx+a)+bcos(πx+b)+4 f(2010)=5 f(2013)=
f(x)=asin(πx+a)+bcos(πx+β)+4,且f(1999)=3,求f(2000)
已知函数f(x)=更号2asin(x-π/4)+a+b 当a
已知函数f(x)=Asin
已知函数f(x)=Asin(2x+a),若函数f(x+π/6)为偶函数,且f(π/6)=4,求f(x)解析式
若函数f(x)=(1+cos2x)/[4sin(π/2+x)]-asinπ/2cos(π-x/2)
1.函数f(X)=asin(X+π/4)+3sin(X-π/4)是偶函数,则a=
若f(x)=asin(x+π/4)+3sin(x-π/4)是偶函数,则实数a=
若f(x)=asin(x+π/4)+3sin(x-π/4)是偶函数,求a
已知函数f(x)=Asin(2x+φ),当x=-π/3时,最小值为-4,
已知函数f(x)=asin(πx+α)+bcos(πx+β)+4,x∈R,且f(2011)=3,则求f(2012)的值
asin(θ+α)+bsin(θ+β)=?化简f(x)=asin(πx+α)+bcos(πx+β)且f(2009)=3,则f(2010)=?
已知函数 f(x)=Asin(π/3x+b),x∈R,A>0,0
f(x)=Asin(x+φ)最大值为1,0
已知函数f(x)=Asin(x+&)(A>0,0
已知函数f[x]=Asin²【ωx+
已知函数f(x)=Asin(x+q) (0