Question

若函数f(x)是周期函数为6的奇函数，则sin[f(-7)+f(1)+π/12]×cos[f(6)+π/12]的值等于

Answer 1

1/4
因为f(x)为奇函数，所以f(0)=0
又因为f(x)周期为6，所以f(-7)=f(-1),f(6)=0
所以原式=sin(π/12)*cos(π/12)=1/2(sin(π/6))=1/4

这是对函数的考察，望答案对你有帮助

Answer 2

f(x)是周期函数为6的奇函数,f(1)=-f(-1)=-f(-7)
所以f(-7)+f(1)=0
f(6)=f(0)=-f(-0)=0
原式=sinπ/12×cosπ/12=1/2sinπ/6=1/4

Answer 3

f(-7)=f(-1)=-f(1);f(6)=f(0)=0
所以原式=sin（π/12)*cos(π/12）=sin（π/6)/2=1/4