若直线的斜率k满足-√3﹤k﹤(√3)/3譬,则该直线的倾斜角a的范围是____.
[0,π/6)∪(2π/3,π)。由斜率k满足-√3﹤k﹤√3/3,-√3﹤tana﹤√3/3,可分为0≤tana﹤√3/3和-√3﹤tana﹤0,再由正切值的单调性可知倾斜角a的范围为[0,π/6]∪(2π/3,π).
若直线的斜率k满足-√3﹤k﹤(√3)/3譬,则该直线的倾斜角a的范围是____.
[0,π/6)∪(2π/3,π)。由斜率k满足-√3﹤k﹤√3/3,-√3﹤tana﹤√3/3,可分为0≤tana﹤√3/3和-√3﹤tana﹤0,再由正切值的单调性可知倾斜角a的范围为[0,π/6]∪(2π/3,π).