5．利用余弦定理，可以解决以下两类问题：

　(1)已知三边，求三角；(2)已知两边和它们的夹角，求第三边和其他两角。

4．利用正弦定理，可以解决以下两类问题：

(1)已知两角和任一边，求其他两边和一角；

(2)已知两边和其中一边的对角，求另一边的对角；有三种情况：

bsinA<a<b时有两解；a=bsinA或a=b时有 解；a<bsinA时无解。

3．余弦定理：a²=b²+c²-2bccosA, ；

证明：如图ΔABC中，

当A、B是钝角时，类似可证。

正弦、余弦定理可用向量方法证明。

要掌握正弦定理、余弦定理及其变形，结合三角公式，能解有关三角形中的问题．

2．正弦定理：

证明：由三角形面积

得

画出三角形的外接圆及直径易得：

1．三角形基本公式：

(1)内角和定理：A+B+C=180°，sin(A+B)=sinC,　 cos(A+B)= -cosC,

cos=sin,　 sin=cos

(2)面积公式：S=absinC=bcsinA=casinB

S= pr = (其中p=,　 r为内切圆半径)

(3)射影定理：a = bcosC + ccosB；b = acosC + ccosA；c = acosB + bcosA

掌握正弦、余弦定理，能初步运用它们解斜三角形。

5．句子翻译

1)　　 护士给这个病人量了体温。(temperature)

2)　　 他回想起他们首次相遇的那一天。(think)

3)　　 我一进房间电话就响了。(than)

4)　　 你能辨别这两种酒的不同吗？(tell)

5)　　 请把这首诗由中文译成法语。(translate)

6)　　 这个商店周五营业到晚上九点钟。(till)

7)　　 让我们为爱德华干杯，祝贺他工作干得漂亮。(toast)

8)　　 我厌烦电视，我们还是出去散散步吧。(tire)

9)　　 由于交通诸塞我们被困住了。(trap)

她深深地被这部小说打动了。(touch)

4．词组填空

for themselves　　 clear his throat　　 even though　　 on top of　 in total　　 in terms of　　 in theory　　 as though　　 there you are　　 tourist attraction

1)　　　　 The professor _______ to get our attention before beginning his lecture.

2)　　　　 It is also good to think ______ what bad things could happen.

3)　　　　 _________, more competition means lower prices for consumers.

4)　　　　 ______________. I’ve been looking for you.

5)　　　　 Pascal went ahead with the experiment _________ he knew it was dangerous.

6)　　　　 He stared at me _______ I were a complete stranger.

7)　　　　 There were probably about 40 people present at the meeting ___________.

8)　　　　 The Statue of Liberty is a major ___________.

9)　　　　 _________ everything else, I now have to go to work first.

10)　　 Parents have to teach their children to think ____________.

3．单项选择

1)　　　　 Only time will ________ if this agreement will bring a lasting peace.

A. speak　 B. tell　　 C. say　　 D. talk

2)　　　　 The phone was ringing, but by the time she _________ indoors, it __________.

A. got; stopped　　 B. had got; stopped　

C. got; had stopped　　 D. had got; had stopped

3)　　　　 “I have to go,” she said, and with _______ she hung up the phone.

A. it　 B. which　 C. that　　 D. whom

4)　　　　 He bought the tickets ________ a friend at the stadium.

A. through　　 B. thorough　　 C. though　　 D. throughout

5)　　　　 Recycling saves energy, ________ acid rain, global warming and air pollution

A. so reduces　　 B. so reducing　　 C. thus reduces　 D. thus reducing

6) --- ______ is it today?　　 --- It’s Tuesday.

　 A. When　　 B. What time　 C. What date　　 D. What day

7) Jack, together with his friends, _______ to climb out of the canyon.

A. decide　 　B. has decided　　 C. are to decide　　 D. are deciding

8) ______ exists music everywhere in our life! Shall we sing together?

　 A. There　　 B. Where　　 C. Wherever　　 D. Therefore

9) The room, _________, is pleasant and airy. I love it very much.

　 A. being small　　 B. it is small　　 C. but small　　 D. though small

10) Language are taught by the direct method, _________ , without using the students’ own language.

　 A. believe it or not　 B. to tell the truth　 C. that’s to say　　 D. generally speaking

2．词形变化

1)　　　　 Exercise is the ideal way to reduce _________ (tense) after a hard day.

2)　　　　 I’ll be ________ (thank) for a good night’s sleep after the busy week I’ve had.

3)　　　　 Many old people are living by ________ (them) and they fell lonely.

4)　　　　 He wrote a _________ (thrill), which told an exciting story about murder or crime.

5)　　　　 I’ve had such a _________ (tire) day. I just want to take a bath and go to bed.

6)　　　　 He works as a ___________ (translate) changes writing into a different language.

7)　　　　 It is ___________ (tradition) not to eat meant on Good Friday().

8)　　　　 We all had to go on a special ___________ (train) course to learn new sales techniques.

9)　　　　 As a seasoned (有经验的) ___________ (travel), I know the value of being able to speak at lease a few words of the local language.

10)　　 He was __________ (terrify) at the thought of being trapped in the woods.