3.7 ã 3.8 æ­£å¼¦åä½å¼¦å®çååºç¨

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# 3.7 ã 3.8 æ­£å¼¦åä½å¼¦å®çååºç¨ - PowerPoint PPT Presentation

3.7 、 3.8 正弦和余弦定理及应用. 一、. 知识归纳. a-b&lt;c a-c&lt;b b-c&lt;a. (3) 边角关系 :. (3) 边角关系 :. ① . 正弦定理. 变形. A. c. b. B. a. C. b 2 +c 2 - a 2. a 2 +b 2 - c 2. c 2 +a 2 - b 2. cosA=. cosC=. cosB=. 2bc. 2ab. 2ca. ② . 余弦定理. a 2 =b 2 +c 2 -2bc·cosA b 2 =c 2 +a 2 -2ca·cosB

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a-b<c a-c<b b-c<a

(3)边角关系:

(3)边角关系:

①.正弦定理

A

c

b

B

a

C

b2+c2 - a2

a2+b2 - c2

c2+a2 - b2

cosA=

cosC=

cosB=

2bc

2ab

2ca

②.余弦定理

a2=b2+c2-2bc·cosA

b2=c2+a2-2ca·cosB

c2=a2+b2-2ab·cosC

2.三角形面积公式:

(其中 r为三角形内切圆的半径)

3.正弦、余弦定理在解三角形 中能解决哪些问题？

(A)等腰三角形 (B)直角三角形

(C)等腰或直角三角形 (D)等腰直角三角形

A

C

A

1.（2010广东文）已知a,b,c分别是△ABC的三个内角A,B,C 所对的边,若a=1,b= , A+C=2B,则sinA=_________________.

(1) 求 · ; (2)若c－b=1,求a的值.

(1) 144

(2) a =5

3 .(2011江苏卷)在△ABC中，角A、B、C所对应的边为 a,b,c

（1）若 求A的值；

（2）若 ，求sinC的值.

3 .(2011江苏卷)在△ABC中，角A、B、C所对应的边为 a,b,c

（1）若 求A的值；

（2）若 ，求sinC的值.