设f(x)实在定义域R上的偶函数,当0≤x<π/2时,f(x)=cos(x+π/3)-1/2,且f(π+π/3)=f(x)
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2010-12-13
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1)f(x)在R上是偶函数,则f(x)=-f(-x)
已知0≤x≤π/2时,f(x)=cos(x+π/3)-1/2;则f(x)=-f(-x)=-cos(-x+π/3)+1/2=cos(x-π/3)+1/2
2)f(31π/6)=f(π+1π/6)=f(1π/6)=-1/2
已知0≤x≤π/2时,f(x)=cos(x+π/3)-1/2;则f(x)=-f(-x)=-cos(-x+π/3)+1/2=cos(x-π/3)+1/2
2)f(31π/6)=f(π+1π/6)=f(1π/6)=-1/2
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