Question

如右图放置的正方形ABCD，AB＝1，A，D分别在x轴、y轴的正半轴(含原点)上滑动，则的最大值是________．

Answer 1

2

令∠OAD＝θ，∵AD＝1，∴OA＝cos θ，OD＝sin θ，∠BAx＝－θ，故x_B＝cos θ＋cos ＝cos θ＋sin θ，y_B＝sin ＝cos θ，∴＝(cos θ＋sin θ，cos θ)，同理可求得C(sin θ，cos θ＋sin θ)，∴＝(sin θ，cos θ＋sin θ)，∴＝(cos θ＋sin θ，cos θ)·(sin θ，cos θ＋sin θ)＝1＋sin 2θ≤2.