myfriend-liang
幼苗
共回答了16个问题采纳率:93.8% 举报
y=2sin(2x+π/6)+2sin(2x-π/3)
=2sin(2x-π/3+π/2)+2sin(2x-π/3)
=2cos(2x-π/3)+2sin(2x-π/3)
=2√2[sin(2x-π/3)cos(π/4)+cos(2x-π/3)sin(π/4)]
=2√2sin(2x-π/3+π/4)=√6
所以sin(2x-π/12)=√3/2=sin(π/3)
∵x∈(0,π)
∴2x-π/12∈(-π/12,2π-π/12)
∴2x1-π/12=π/3,2x2-π/12=2π/3,
∴x1=5π/24,x2=9π/24
所以交点有2个,分别是(5π/24,√6),(9π/24,√6)
1年前
追问
5