Question

高中数学必修四，三角函数，填空题求过程解答，谢谢，

Answer 1

已知函数f(x)=sin(wx+π/3)(w>0)，f(π/6)=f(π/3)且f(x)在区间(π/6, π/3)内有最小值，无最大值，求w

解析：∵函数f(x)=sin(wx+π/3)(w>0)，f(π/6)=f(π/3)且f(x)在区间(π/6, π/3)内有最小值，无最大值
则函数f(x)初相为π/3，离Y轴最近的极值点为最大值点
最小值点：wx+π/3=2kπ+3π/2==>x=2kπ/w+7π/(6w)
要使f(π/6)=f(π/3)且f(x)在区间(π/6, π/3)内有最小值，无最大值
须使x=π/6,x=π/3关于x=7π/(6w)，即x=π/4对称
令7π/(6w)=π/4==>w=14/3
∴f(x)=sin(14/3x+π/3)