题目

已知角的顶点在坐标原点，始边与x轴的正半轴重合，，角的终边与单位圆交点的横坐标是，角的终边与单位圆交点的纵坐标是，（1）求；（2）求；（3）求. 答案：【答案】（1）（2）（3）【解析】（1）利用三角函数的定义，得，再用平方关系求解.（2）利用三角函数的定义，得，根据且，确定，再用平方关系求解.（3）根据（1）（2）的结论，利用角的变换求解.（1）根据题意，，又因为，所以.（2）根据题意，，且，所以，.（3）由（1）（2）得.Directions: Read the following passage. Answer the questions according to the information given in the passage and required words limit. Write your answers on your answer sheet. A 10-year-old boy decided to study judo despite the fact that he had lost his left arm in a terrible car accident. The boy began lessons with an old Japanese judo master. The boy was doing well, so he couldn't understand why, after three months of training, the master had taught him only one move. "Sensei," the boy finally said, "shouldn't I be learning more moves?" "This is the only move you know, but this is the only move you'll ever need to know," the sensei replied. Not quite understanding, but believing in his teacher, the boy kept training. Several months later, the sensei took the boy to his first tournament.Surprising himself, the boy easily won his first two matches. The third match proved to be more difficult, but after some time, his opponent became impatient and charged; the boy deftly used his one move to win the match. Still amazed by his success, the boy was now in the finals. This time, his opponent was bigger, stronger, and more experienced. For a while, the boy appeared to be overmatched. Concerned that the boy might get hurt, the referee called a timeout. He was about to stop the match when the sensei intervened."No," the sensei insisted, "let him continue." Soon after the match resumed, his opponent made a big mistake: he dropped his guard. Instantly, the boy had won the match and the tournament. He was the champion. On the way home, the boy and sensei reviewed every move in each and every match. Then the boy gathered the courage to ask what was really on his mind. "Sensei, how did I win the tournament with only one move?" You won for two reasons," the sensei answered. "First, you've almost mastered one of the most difficult throws in all of judo. Second, the only known defense for that move is for your opponent to grab your left arm."小题1:How did the judo master teach the boy? (no more than 8 words) __________________________________________________________________________小题2: Why did the referee call a timeout? (no more than 9 words) __________________________________________________________________________小题3:What were the reasons for the boy’s winning the champion? (no more than 20 words) __________________________________________________________________________小题4:What can we learn from the short story? (no more than 8 words) __________________________________________________________________________