Question

f(X)是定义在R上的周期是π的偶函数,当x属于[0,π/2]时f(X)=sinx,则f(5π/3)=

求解答过程

Answer 1

f(5π/3)= f(5π/3-2π)=f(-π/3)
因为f是偶函数。所以
f(-π/3)=f(π/3)
f(π/3)=sin（π/3）=√3/2

Answer 2

∵f(x)为R上的偶函数且T=π
∴f(x)=f(-x)
∵x∈[0 π/2]时，f(x)=sinx
f(x+π)=f(x)=sinx
∵sin(x+π)=sin(-x)=-sinx
∴要使sinx=sin(-x)那么f(x)=/sinx/
∴f(5π/3)= f(2π/3)=/sin(2π/3)/=3½／2