已知直线l经过点P（1,1）,倾斜角α=π/6,写出直线l的参数方程过程详细点,

∵直线过点P（1,1）,倾斜角为π/6,
∴直线方程为y-1=tan(π/6)(x-1)
(y-1)/sin(π/6) =(x-1)/cosπ/6
令t=(y-1)/sin(π/6) =(x-1)/cosπ/6
则x=1+t×cosπ/6,y=1+t×sin(π/6)
∴参数方程为x=1+(√3t)/2,y=1+t/2,（t为参数）.