问题 选择题

在△ABC中,“A>B”是“sinA>sinB”成立的(  )

A.充要条件

B.2充分部必要条件

C.必要不充分条件

D.既不充分也不必要条件

答案

1°由题意,在△ABC中,“A>B”,由于A+B<π,必有B<π-A

若A,B都是锐角,显然有“sinA>sinB”成立,

若A,B之一为锐角,必是B为锐角,此时有π-A不是钝角,由于A+B<π,必有B<π-A≤

π
2
,此时有sin(π-A)=sinA>sinB

综上,△ABC中,“A>B”是“sinA>sinB”成立的充分条件

2°研究sinA>sinB,若A不是锐角,显然可得出A>B,若A是锐角,亦可得出A>B,

综上在△ABC中,“A>B”是“sinA>sinB”成立的必要条件

综合1°,2°知,在△ABC中,“A>B”是“sinA>sinB”成立的充要条件,

故选A

配伍题 B型题
阅读理解

The way people hold to the belief that a fun-filled, and pain-free life equals happiness actually reduces their chances of ever attaining real happiness. If fun and pleasure are equal to happiness then pain must be equal to unhappiness. But in fact, the opposite is true: more often than not things that lead to happiness involve some pain.

As a result, many people avoid the very attempts that are the source of true happiness. They fear the pain inevitably(不可避免的) brought by such things as marriage, raising children, professional achievement, religious commitment (义务), self - improvement.

Ask a bachelor(单身汉) why he resists marriage even though he finds dating to be less and less satisfying. If he is honest he will tell you that he is afraid of making a commitment. For commitment is in fact quite painful. The single life is filled with fun, adventure, excitement. Marriage has such moments, but they are not its most distinguishing features.

Couples with infant children are lucky to get a whole night’s sleep or a three - day vacation. I don’t know any parent who would choose the word fun to describe raising children. But couples who decide not to have children never know the joys of watching a child grow up or of playing with a grandchild.

Understanding and accepting that true happiness has nothing to do with fun is one of the most liberating realizations. It liberates time: now we can devote more hours to activities that can genuinely increase our happiness. It liberates (解放)money: buying that new car or those fancy clothes that will do nothing to increase our happiness now seems pointless. And it liberates us from envy: we now understand that all those who are always having so much fun actually may not be happy at all.

小题1:According to the author, a bachelor resists marriage chiefly because _______ .

A.he is reluctant to take on family responsibilities

B.he believes that life will be more cheerful if he remains single

C.he finds more fun in dating than in marriage

D.he fears it will put an end to all his fun adventure and excitement小题2:From the last paragraph, we learn that envy sometimes stems from ________ .

A.hatred

B.misunderstanding 

C.prejudice

D.ignorance小题3:What is the author trying to tell us?

A.Happiness often goes hand in hand with pain.

B.One must know how to attain happiness.

C.It is important to make commitments.

D.It is pain that leads to happiness.