(理)设α∈(0,π),函数f(x)的定义域为[0,1],且f(0)=0,f(1)=1,对定义域内任意的x,y,满足f( x+y 2 )=f(x)sinα+(1-sinα)f(y). (1)试用α表示f( 1 2 ),并在f( 1 2 )时求出α的值; (2)试用α表示f( 1 4 ),并求出α的值; (3)n∈N时,a n = 1 2 n ,求f(a n ),并猜测x∈[0,1]时,f(x)的表达式. (文)已知向量 OA =(3,-4), OB =(6,-3), OC =(5-m,-3-m) (1)若点A、B、C不能构成三角形,求实数m应满足的条件. (2)若△ABC为直角三角形,求m的取值范围.