您所在的当前位置：高中数学试题 >

任意角三角函数的概念

> 已知向量 a =(sinx，-1)， b =( 3 cosx，- 1 2 )，函数 f(x)=( a + b )• a -2．（Ⅰ）求函数f（x）的最小正周期T；（Ⅱ）已知a、b、c分别为△ABC内角A、B、C的对边，其中A为锐角， a=2 3 ，c=4，且f（A）=1，求A，b和△ABC的面积S．

问题：

发布时间：2024-09-10

已知向量

a

=(sinx，-1)，

b

=(

3

cosx，-

1

2

)，函数 f(x)=(

a

+

b

)•

a

-2．
（Ⅰ）求函数f（x）的最小正周期T；
（Ⅱ）已知a、b、c分别为△ABC内角A、B、C的对边，其中A为锐角， a=2

3

，c=4，且f（A）=1，求A，b和△ABC的面积S．

参考答案：

提问用户：au***C4m

可能感兴趣的题目：

1 据报道，美国宇航局发射的“勇气”号和“机遇”号孪生双子火星探测器在2004年1月4日和1月25日相继带着地球人的问候在火星着陆。假设火星和地球绕太阳的运动可以近似看作同一平面内同方向的匀速圆周运动，已知火星的轨道半径r 1=2.4×10 11m，地球的轨道半径r 2=1.5×10 11m，如图所示，从图示的火星与地球相距最近的时刻开始计时，请估算火星再次与地球相距最近需多长时间：（） A．1.4年 B．4年 C．2.0年 D．1年
2 阅读理解。 A man went to a barbershop to have his hair and beard cut as always. He started to have a good conversation with the barber who attended him. They talked about so many things on various subjects. Suddenly, they touched the subject of God. The barber said," I don"t believe that God exists as you say so."" Why do you day that?" asked the client (顾客)." well, it"s so easy; you just have to go out in the street to realize that God does not exist.""Oh, tell me."" If God existed, would there be so many sick people? Would there be so many abandoned children? If God existed, there would be neither suffering nor pain. I can"t think of God who permits all of these things." The client stopped for a moment thinking but he didn"t want to respond so as to prevent an argument. The barber finished his job and the client went out of the shop. Just after he left the barbershop, he saw a man in the street with long hair and beard. Then the client again entered the barbershop and he said to the barber," Knowing what? Barbers do not exist." " How come they don"t exist?" asked the barber,"Well I am here and I am a barber.""No!" the client exclaimed,"They don"t exist because if they did there would be no people with long hair and beard like that man who walks in the street." "Ah, barbers do exist, what happens is that people do not come to me." "Exactly!" affirmed the client. "That"s the point. God does exist, what happens is that people don"t go to him for help. That"s why there"s so much pain and suffering in the world." 1. The client was trying to prove that _____. A. God exists B. God permits suffering and pain B. barbers do not exist D. people have to look for God 2. According to the barber, if God existed, _____. A. there would be so many sick people B. there would be deserted children C. there would be no suffering in the world D. there would be no people with long hair and beard in the street 3. Why did the man in the street wear long hair and beard? A. he was poor and had no money to go to the barber"s B. he was not willing to go to the barber"s C. it is fashionable to wear long hair and beard D. it is not mentioned in the passage 4. It can be inferred from the passage that _____. A. the barber wad talkative B. the client was very clever C. God does exist D. God does not exist
3 做匀减速直线运动的质点，它的加速度大小为a，初速度大小为v 0，经过时间t速度减小到零，则它在这段时间内的位移大小可用下列哪些式子表(　　)． A．v0t ＋at2 B．v0t －at2 C． D．at2
4 The boss insisted that every minute ______ made full use of ______ the work well. A．be ; to do B．was ; doing C．be ; doing D．was ; to do
5 下列现象中，不属于摩擦起电的是 A.在磁铁上摩擦过的小刀能把大头针吸引起来 B.用梳过头发梳子靠近细细的自来水水流时，水流被吸引过来 C.用干燥的毛刷刷毛料衣服时，毛刷上吸附着许多细微脏物 D.在干燥的天气中脱毛衣时，听到轻微的“噼啪”声，甚至在夜晚能看见火花
6 阅读理解。　Our boat floated on, between walls of forest which were too thick to allow us a view of the land we were passing through, although we knew from the map that our river must from time to time be passing through chains of hills which crossed the jungle plains. Nowhere did we find a place where we could have landed: where the jungle did not actually spread down into the river, banks of soft mud prevented us going ashore. In any case, what would we have gained by landing? The country was full of snakes and other dangerous creatures and the jungle was so thick that one would be able to advance only slowly, cutting one"s way with knives the whole way. So we stayed in the boat, hoping that when we reached the sea, a friendly fisherman would pick us up and take us to civilization. 　　 We lived on fish, any fruit and nuts we could pick up out of the water. As we had no fire, we had to eat everything, including the fish, raw. I had never tasted raw fish before, and I must say I did not much enjoy the experience: perhaps sea-fish which don"t live in the mud are less tasteless. After eating my fish, I lay back and dreamed of such things as fried chicken and rice, and ice cream. In the never-ending heat of the jungle, ice cream was a particularly frequent dream.　　 As for water, there was a choice. We could drink the muddy river water, or die of thirst. We drank the water. Men who have just escaped what had appeared to certain death lose all worries about such small things as diseases caused by dirty water. In fact, none of us suffered from any illness as a result. One day we passed another village, but fortunately nobody saw us. We did not wish to risk being taken prisoners a second time: we might not be so lucky as to escape in a stolen boat again. 1. The only thing that they could see in the boat was _______. 　　 A. chains of hills 　　　　 B. high walls C. vast land 　　　　　　　 D. tall trees 　 2. They were prevented from landing because they could not _______. 　　 A. find the place marked on the map 　　　　 B. go through the thick forest 　　 C. go across the soft mud 　　　　　　　　　 D. see the plains 　 3. This passage is mainly about ______. 　　 A. the problem of landing 　　　　 B. a terrible experience 　　 C. walls of forest　　　　　　　　 D. the fishermen"s worries 　 4. Which of the following is NOT true according to the passage? 　　 A. The author and his partners were trapped during scientific exploration. 　　 B. They were floating on a small boat in the jungle without help. 　　 C. The dirty water they drank didn"t threaten their lives. 　　 D. They had no food or drinking water prepared.
7 下图示意云南省昆明附近产业转化的构想，Ⅰ表示烟草业的变化，Ⅱ表示鲜花业的变化，读图回答各题。小题1:该区域发展花卉业(“彩色农业”)的气候资源优势是 A．太阳辐射强 B．“四季如春”，降水丰沛 C．终年温和多雨 D．夏季炎热干旱，冬季温和多雨小题2:该区域发展成为花卉业基地的优势是 A．廉价劳动力，土地价格较低 B．技术力量强 C．消费市场广阔 D．交通便利，利于出口小题3:要解决保鲜、开发新品种等问题，从而使花卉业具有国际优势，最重要的途径是 A．扩大生产规模 B．技术创新 C．整治水环境 D．提高劳动力素质小题4:该产业转化的意义有 ①减少运输成本 ②使卷烟产量增加 ③既有益生态，又美化生活 ④消除不可持续发展隐患 A．①② B．③④ C．①③ D．②④
8 向盛有KI溶液的试管中滴加氯水后再加入少许CCl 4，充分振荡后CCl 4层呈紫色。如果继续向试管中滴加氯水，充分振荡，CCl 4层又会逐渐变浅，最后变成无色。根据以上信息完成下列填空： (1)写出并配平CCl 4层由紫色变成无色的化学反应方程式，并用双线桥法标出电子转移的方向和数目： (2)实验中的有机溶剂CCl 4还可以用代替。 A．苯 B．煤油 C．酒精 D．醋酸 (3)若把KI换成KBr，则CCl 4层变为色；继续滴加氯水，CCl 4层的颜色没有变化。则Cl 2、HIO 3、HBrO 3氧化性由强到弱的顺序是。 (4)加碘盐中含碘量为20mg～50mg/kg。制取加碘盐(含KIO 3的食盐)1000kg，若用KI与Cl 2反应制KIO 3，至少需要消耗Cl 2________L(标准状况，计算结果保留1位小数)。
9 蹦床是运动员在一张绷紧的弹性网上蹦跳、翻滚并做各种空中动作的运动项目。一个质量为60kg的运动员，从离水平网面3.2 m高处自由下落，着网后沿竖直方向蹦回离水平网面5.0 m高处。已知运动员与网接触的时间为1.2s。若把这段时间内网对运动员的作用力当做恒力处理，求此力的大小。（g取10 m/s 2）
10 关于亚洲各地民俗习惯和自然条件的关系，正确的解释是 A.也门人居住帐篷，身着宽大袍子，过着游牧生活--高纬度地区，气候严寒 B.加里曼丹岛的达雅克人多住高脚屋--多地震 C.孟加拉人以船为交通工具--地势低平，河网密布 D.日本人的住房大多是平顶--气候湿热的自然条件

已知向量 a =(sinx，-1)， b =( 3 cosx，- 1 2 )，函数 f(x)=( a + b )• a -2． （Ⅰ）求函数f（x）的最小正周期T； （Ⅱ）已知a、b、c分别为△ABC内角A、B、C的对边，其中A为锐角， a=2 3 ，c=4，且f（A）=1，求A，b和△ABC的面积S．

可能感兴趣的题目：