将函数f（x）=sin1／4x•sin1／4（x+2派）•sin1／2（x+3派）在区间（0,正无穷）内的全部极值点按从小到大顺序排成数列{an},求通项

Question

将函数f（x）=sin1／4x•sin1／4（x+2派）•sin1／2（x+3派）在区间（0,正无
穷）内的全部极值点按从小到大顺序排成数列{an},求通项

Answer 1

f(x)=sin1/4xsin1/4(x+2拍)sin1/2(x+3拍)
=-sin(x/4)cos(x/4)cos(x/2)
=-1/2sin(x/2)cos(x/2)
=-1/4sinx
∴将f(x)在区间(0,+∞)内的全部极值点按从小到大的顺序排成数列{an}(n属于N*),数列{an}的通项公式an=(2n-1) 拍/2