已知x属于R,f(x)=1/2sin(2Wx+2α)(W>0,0<α<π/2)且f(x)的最小正周期为π,f(π/8)=1/4,求w和α的值
问题描述:
已知x属于R,f(x)=1/2sin(2Wx+2α)(W>0,0<α<π/2)且f(x)的最小正周期为π,f(π/8)=1/4,求w和α的值
答
2w=2π/π=2
w=1
f(π/8)=1/2sin(2Wx+2α)=1/2sin(π/4+2α)=1/4
sin(π/4+2α)=1/2
π/4+2α=π/6
a=-π/24 or a=23π/24可α是>0小于π/2的π/4+2α=π-π/6a=7/24π