已知f(x)=sin(x+φ)+cos(x+φ)为偶函数,则φ等于

f(x)=sin(x+φ)+cos(x+φ)
f(x)=√2*[sin(x+φ)*√2/2+cos(x+φ)*√2/2]
f(x)=√2*sin(x+φ+π/4)
sinx函数向左平移φ+π/4个单位得到偶函数
当φ+π/4∈[π/2+kπ]
φ∈[π/4+kπ]
A
f(x)=asinx-bcosx
f(x)=√(a^2+b^2) sin(x-α) cosα=a/√(a^2+b^2) sinα=b/√(a^2+b^2)
π/4得最小值
则π/4-α∈{-π/2+2kπ}
α∈{3π/4+2kπ}
f(x)=√(a^2+b^2) sin(x-3π/4)
y=f(3π/4-x)=√(a^2+b^2) sin(-x)
y=-√(a^2+b^2) sinx
为奇函数,关于(π,0)对称
D

B
sin(x+φ)+cos(x+φ)=cosπ/4sin(x+φ)+sinπ/4cos(x+φ)=sin(x+φ+π/4)
它是偶函数，则说明是cos,那么φ=π/4再加上周期2kπ+π/4

A
利用sinx+cosx=根号2*sin(x+π/4)
得到f(x)=sin(x+φ)+cos(x+φ)=根号2*sin(x+φ+π/4)
所以已知f(x)为偶函数，则sin(-x+φ+π/4)=sin(x+φ+π/4)
所以sin(x+φ+π/4)-sin(-x+φ+π/4)=sin(x+φ+π/4)+sin(x-φ-π/4)=0
所以利用和差化积的公式...