若f(x)=asin(x+π/4)+3sin(x-π/4)是偶函数,则实数a的值为

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lingyun167 共回答了18个问题 | 采纳率88.9%: 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; 1年前

雨中想你共回答了42个问题 | 采纳率: 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)...; 1年前

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F(x)=asin(x+π/4)+3sin(x-π/4)是奇函数,则F(x)的最大值是 aaaaaa6071年前1: ychgen 共回答了22个问题 | 采纳率95.5%

因为它是奇函数,所以f(0)=-f(0)所以f(0)=0,得到a=3,之后提出3,两个sin和差化积得到F（x）=6sinxcosπ/4,所以最大为3*根号2

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