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?
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![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?](/uploads/image/z/6916161-57-1.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3DAsin%282x%2BB%29%28A%3E0%29%2C%E4%B8%94%E5%AF%B9%E4%BB%BB%E6%84%8F%E7%9A%84%E5%AE%9E%E6%95%B0x%E6%BB%A1%E8%B6%B3f%28x%2B%E6%B4%BE%2F12%29%3Df%28%E6%B4%BE%2F12-x%29%2C%E5%88%99f%28%E6%B4%BE%2F3%29%E7%9A%84%E5%80%BC%E4%B8%BA%3F)
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?
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?
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?
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)
=Asin(k+1)π=0
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