题目

Brenda Bongos was a happy, artistic girl. She had one big ambition—to play the drums in a band. But one big problem lay in her way. To be good enough to play in a band, Brenda had to practice a lot, but she lived next-door to a lot of old people. Many of them are sick. She knew that the sound of beating drums would really get on their nerves. So, she had tried playing in the strangest places: a basement, a kitchen, and even in a shower. But there was always someone it would annoy.     One day, while watching a science documentary on TV, she heard that sound cannot travel in space,如图，在平面直角坐标系xoy中，A为以原点O为圆心的单位圆O与x正半轴的交点，在圆心角为 的扇形AOB的弧AB上任取一点 P，作 PN⊥OA于N，连结PO，记∠PON=θ． （1）设△PON的面积为y，使y取得最大值时的点P记为E，点N记为F，求此时 的值；（2）求k=a| || |+ （a∈R，E 是在（1）条件下的点 E）的值域．