题目

已知函数,(1)求的定义域;(2)设α是第四象限的角,且tanα=,求f(α)的值. 答案：思路分析：本题主要考查了三角函数的性质,同角三角函数基本关系式,倍角公式等基础知识.由正切值及角的范围可求出角的正,余弦值.解：(1)由cosx≠0得x≠kπ+,k∈Z,故f(x)的定义域为{x｜x≠kπ+,k∈Z}.(2)∵α是第四象限角,tanα=,则,sinα=-1-cos2α=.故==2(cosα-sinα)=.方法归纳 函数的定义域是指使函数有意义的自变量2、      I was in a rush as always, but this time it was for an important date I just couldn’t be late for! I found myself at a checkout counter behind an elderly woman seemingly in no hurry as she paid for her groceries. A PhD student with not a lot of money, I had hurried into the store to pick up some flowers. I was in a huge rush, thinking of my upcoming evening. I did not want to be late for this date.      We were in Boston, a place not always known for small conversation between strangers. The woman stopped unloading her basket and looked up at me. She smiled. It was a nice smile-warm and reassunring-and I retuned her gift by smiling back.      “Must be a special lady,” whoever it is that will be getting those beautiful flowers,” she said.      “Yes, she’s special,” I said, and then to my embarrassment, the words kept coming out. “It‘s only our second date, but somehow I am just having the feeling she’s‘the one ，’”jokingly, I added, “The only problem is that I can’t figure out why she’d want to date a guy like me.”      “Well, I think she’s very lucky to have a boyfriend who brings her such lovely flowers and who is obviously in love with her,” the woman said .”My husband used to bring me flowers every week-even when tines were tough and we didn’t have much money. Those were incredible days; be was very romantic and-of course- I miss him since he’s passed away.”       I paid for my flowers as she was gathering up her groceries. There was no doubt in my mind as I walked up to her. I touched her on the shoulder and said “You were right, you know. These flowers are indeed for a very special lady.” I handed the flowers and thanked her for such a nice conversation.       It took her a moment to realize that I was giving her the flowers I had just purchased. “You have a wonderful evening,”I said. I left het with a big smile and my heart warmed as I saw her smelling the beautiful flowers.       I remember being slightly late for my date that night and telling my girlfriend the above story. A couple of years later, when I finally worked up the courage to ask her to marry me, she told me that this story had helped to seal it for her-that was the night than I won her heart .  41．Why was the writer in a hurry that day? A. He was to meet his girlfriend.        B. He had to go back to school soon. C. He was delayed by an elderly lady.    D. He had to pick up some groceries. 42．What does the underlined phrase “her gift” (Paragraph 2 ) refer to? A. Her words.   B. Her smile.    C. Her flowers.    D. Her politeness. 43．Why did the writer give his flowers to the elderly lady? A. She told him a nice story.       B. She allowed him to pay first. C. She gave him encouragement.   D. She liked flowers very much. 44．What is the message conveyed in the story? A. Flowers are important for a date.      B. Small talk is helpful. C. Love and kindness are rewarding.     D. Elderly people deserve respecting.