(1) 當(dāng)x∈(-π/2,0]時,-x∈[0,π/2),所以　f(x)=-f(-x)=-sin(-x)=sinx；
當(dāng)x=-π/2時,f(x)=f(-π/2)=f(-π/2+π)=f(π/2)=1；
當(dāng)x∈[-π,-π/2)時,x+π∈[0,π/2],所以　f(x)=f(x+π)=sin(x+π)=-sinx；
從而　　┌-sinx,x∈[-π,-π/2),
f(x)= │ 1,x=-π/2,
　└sinx,x∈(-π/2,0]
(2)當(dāng)x∈(-π/2,π/2]時,f(x)=sinx,令sinx≥1/2,解得　π/3≤x≤π/2,
因為周期為π,所以x的取值范圍是
kπ+π/3≤x≤π/2+kπ　,k是整數(shù)．