问题 选择题
θ=
π
3
”是“cosθ=
1
2
”的(  )
A.充分不必要条件B.必要不充分条件
C.充要条件D.既不充分也不必要条件
答案

由题意“θ=

π
3
”成立时,一定有“cosθ=
1
2
”成立,故“θ=
π
3
”是“cosθ=
1
2
”充分条件;

又“cosθ=

1
2
”时,可得θ=2kπ±
π
3
,k∈z,故“θ=
π
3
”不是“cosθ=
1
2
”的必要条件.

综上“θ=

π
3
”是“cosθ=
1
2
”的充分不必要条件

故选A.

阅读理解

In the following article, some sentences or paragraphs have been removed. For questions 1 to 5, choose the

most suitable one from the list AF to fit into each of the numbered gaps. There is ONE which does not fit in

any of the gaps.

     Most of the people who appear most often and most gloriously in the history books are great conquerors

and generals, whereas the people who really helped civilization forward are often never mentioned at all. We

do not know who first set a broken leg, or launched a seagoing boat, or calculated the length of the year?

but we know all about the killers and destroyers. People think a great deal of them, so much so that on all the

highest pillars in the great cities of the world you will find the figure of a conqueror or a general.

     1. It is just possible they are, but they are not the most civilized. Animals fight? so do savages? hence to

be good at fighting is to be good in the way in which an animal or a savage is good, but it is not to be civilized.

     2. People fight to settle quarrels. Fighting means killing, and civilized peoples ought to be able to find some

way of settling their disputes other than by seeing which side can kill off the greater number of the other side,

and then saying that that side which has killed most has won.

     3. That is what the story of mankind has on the whole been like. Even our own age has fought the two

greatest wars in history, in which millions of people were killed. And while today it is true that people do not

fight and kill each other in the streets, nations and countries have not learnt to do this yet, and still behave like

savages. But we must not expect too much. After all, the race of men has only just started. From the point of

view of evolution, human beings are very young children indeed, babies, in fact, of a few months old.

     4. These figures are difficult to grasp? so let us scale them down. Suppose that we reckon the whole past

of living creatures on the earth as one hundred years? then the whole past of man works out at about one

month, and during that month there have been civilizations for between seven and eight hours.

     5. Taking man' civilized past at about seven or eight hours, we may estimate his future at about one hundred

thousand years. Thus mankind is only at the beginning of its civilized life, and as I say, we must not expect

too much. The past of 8 man has been on the whole a pretty beastly business, a business of fighting and killing.

We must not expect even civilized peoples not to have done these things. All we can ask is that they will

sometimes have done something else.

     [A] Even being good at getting other people to fight for you and telling them how to do it most efficiently-

this, after all, is what conquerors and generals have done-is not being civilized.

     [B] And I think most people believe that the greatest countries are those that have beaten in battle the

greatest number of other countries and ruled over them as conquerors.

     [C] We have got to the stage of keeping the rules and behaving properly in daily life. However, every year

conflicts between countries and nations are still claiming thousands of lives.

     [D] And not only has won, but, because it has won, has been in the right. For that is what going to war

means? it means saying that might is right.

     [E] So you see there has been little time to learn in, but there will be oceans of time in which to learn better.

     [F] Scientists reckon that there has been life of some sort on the earth in the form of jellyfish and that kind

of creature for about twelve hundred million years? but there have been men for only one million years, and

there have been civilized men for about eight thousand years at the outside.

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