您所在的当前位置：高中数学试题 >

任意角三角函数的概念

> 已知 a =(cosx+sinx，sinx)， b =(cosx-sinx，2cosx)，设 f(x)= a • b ．（Ⅰ）求函数f（x）的最小正周期；（Ⅱ）当 x∈[- π 4 ， π 4 ]时，求函数f（x）的最大值，并指出此时x的值．

问题：

发布时间：2024-09-13

已知

a

=(cosx+sinx，sinx)，

b

=(cosx-sinx，2cosx)，设 f(x)=

a

•

b

．
（Ⅰ）求函数f（x）的最小正周期；
（Ⅱ）当 x∈[-

π

4

，

π

4

]时，求函数f（x）的最大值，并指出此时x的值．

参考答案：

提问用户：A6***k9P

可能感兴趣的题目：

1 下列各组离子一定能大量共存的是 [ ] A．加入铝粉有氢气产生的溶液中：Na +、K +、SO 4 2-、Cl - B．含有大量硝酸根离子的溶液中：H +、Fe 2+、SO 4 2-、Cl - C．c（H +）/c（OH -）=l×10 -10的溶液中：NH 4 +、K +、Ca 2+、Cl - D．水电离的c（H +）=l×10 -12mol/L的溶液中：Na +、K +、HCO 3 -、Cl -
2 如图所示，当滑片P向a端移动时，电路中电流表与电压表变化的情况是 A.两表读数均变大 B.两表读数均变小 C.A表变大，V表变小 D.A表变大，V表不变
3 Before the firemen arrived, the whole building had already been completely _______ in the big fire. A．destroyed B．wounded C．damaged D．injured
4 阅读理解。 Looking back on my childhood, I am convinced that naturalists are born and not made. Although we were all brought up in the same way, my brothers and sisters soon abandoned their pressed flowers and insects. Unlike them, I had no ear for music and languages. I was not an early reader and I could not do mental arithmetic. Before World War Ⅰwe spent our summer holidays in Hungary. I have only the dim memory of the house we lived in, of my room and my toys. Nor do I recall clearly the large family of grandparents, aunts, uncles and cousins who gathered next door. But I do have a clear memory of the dogs, the farm animals, the local birds, and above all, the insects. I am a naturalist, not a scientist. I have a strong love of the natural world and my enthusiasm led me into varied investigations .I love discussing my favorite topics and enjoy burning the midnight oil while reading about other people"s observations and discoveries. Then something happens that brings these observations together in my conscious mind. Suddenly you fancy you see the answer to the riddle, because it all seems to fit together. This has resulted in my publishing 300 papers and books, which some might honor with the title of scientific research. But curiosity, a keen eye, a good memory and enjoyment of the animal and plant world do not make a scientist:one of the outstanding and essential qualities required is selfdiscipline, a quality I lack. A scientist requires not only selfdiscipline, but hard training, determination and a goal. A scientist, up to a certain point, can be made. A naturalist is born. If you can combine the two, you get the best of both worlds. 1.The first paragraph tells us the author________. A. was interested in flowers and insects in his childhood B. lost his hearing when he was a child C. didn"t like his brothers and sisters D. was born to a naturalist"s family 2. The author can"t remember his relatives clearly because________. A. he didn"t live very long with them B. the family was extremely large C. he was too young when he lived with them D. he was fully occupied with observing nature 3.Which of the following statements is TRUE according to the passage? A. The author is a naturalist, but not a scientist. B. The author is a scientist as well as a naturalist. C. The author is first of all a scientist. D. The author is neither a naturalist nor a scientist. 4.The author says that he is a naturalist rather than a scientist probably because he thinks he________. A. has a great deal of trouble doing mental arithmetic B. lacks some of the qualities required of a scientist C .just reads about other people"s observations and discoveries D. comes up with solutions in a most natural way
5 It was the principles I learned from my reading ____enabled me to get bigger and better jobs. A．that B．which C．what D．who
6 下列哪一项不是中东地区战争冲突的导火索 A.“三洲五海”之地 B.世界石油宝库 C.人民生活贫困 D.宗教背景复杂
7 已知等腰三角形的腰长、底边长分别是一元二次方程x 2-7x＋10=0的两根，则该等腰三角形的周长是 A.9或12 B.9 C.12 D.21
8 使用滑轮匀速提起重物时，下列关于绳子所受的拉力F与物体重力G的关系判断中，一定错误的是（不计滑轮的重力及绳子与滑轮间的摩擦） A.F=G/2 B.F=G C.F＜G D.F＞G
9 （14分）已知向量 =（，1）， =（x，x 2）， =（－3，－x 2+x），函数 f（ x）= ·（ + ）．（1）求函数 f（ x）的解析式与定义域；（2）求函数 f（ x）的值域．
10 下列各组离子在强酸性溶液中能大量共存的是 [ ] A．Ba 2+ Na + SCN - Fe 3+ B． Mg 2+ Cl － Al 3+ SO 4 2－ C．K + Cl － HCO 3 － NO 3 － D．Ca 2+ Na + Fe 3+ AlO 2 －

已知 a =(cosx+sinx，sinx)， b =(cosx-sinx，2cosx)，设 f(x)= a • b ． （Ⅰ）求函数f（x）的最小正周期； （Ⅱ）当 x∈[- π 4 ， π 4 ]时，求函数f（x）的最大值，并指出此时x的值．

可能感兴趣的题目：

已知

a

=(cosx+sinx，sinx)，

b

=(cosx-sinx，2cosx)，设 f(x)=

a

•

b

．
（Ⅰ）求函数f（x）的最小正周期；
（Ⅱ）当 x∈[-

π

4

，

π

4

]时，求函数f（x）的最大值，并指出此时x的值．