已知函数f(x)=Asin(2x+B)(A>0),且对任意的实数x满足f(x+派/12)=f(派/12-x),则f(派/3)的值为?

题目

已知函数f(x)=Asin(2x+B)(A>0),且对任意的实数x满足f(x+派/12)=f(派/12-x),则f(派/3)的值为?

答案

f(x)对任意的实数x满足f(x+π/12)=f(π/12-x),说明f(x)以x=π/12为对称轴,也即f(x)在x=π/12处达到最高点或最低点,因此,当x=π/12时,2x+B=kπ+π/2(k∈Z),解得B=kπ+π/3(k∈Z)所以,f(π/3)=Asin(2π/3+kπ+π/3)=As...