向量AC·向量BC
=(cosα-3,sinα)·(cosα,sinα-3)
=1-3(cosα+sinα)
=-1
得cosα+sinα=2/3
√2sin(α+π/4)=2/3
∴sin(α+π/4)=√2/3
|向量OA-向量OC|²=13
OA²+OC²-2*OA*OC*cos∠AOC=13
9+1-6*cos∠AOC=13
cos∠AOC=-1/2
∴∠AOC=2π/3