直线l：2x+1+sinθ/2sinθ×y+3=0,求直线l的倾斜角范围

Question

直线l：2x+1+sinθ/2sinθ×y+3=0,求直线l的倾斜角范围

Answer 1

2x+1+sinθ/2sinθ×y+3=0,
y=-4sinθ/(1+sinθ)x -6sinθ/(1+sinθ)
k=-4sinθ/(1+sinθ)
=[-4(sinθ+1)+4]/(1+sinθ)
=-4 +4/(1+sinθ)
-1≤sinθ≤1
所以
k≥-4+4/2=-4+2=-2
倾斜角范围是：[0,π/2)U（π/2,π-arctan2]