11 x1 t04 06 cosine rule (2013)

21
Cosine Rule A B C a b c x

Upload: nigel-simmons

Post on 04-Jul-2015

477 views

Category:

Education


1 download

TRANSCRIPT

Page 1: 11 x1 t04 06 cosine rule (2013)

Cosine RuleA

B Ca

bc

x

Page 2: 11 x1 t04 06 cosine rule (2013)

Cosine RuleA

B C

h

a

bc

x

Page 3: 11 x1 t04 06 cosine rule (2013)

Cosine RuleA

B C

h

a

bc

2 2 2h b x

x

Page 4: 11 x1 t04 06 cosine rule (2013)

Cosine RuleA

B C

h

a

bc

2 2 2h b x

x

22 2c h a x

Page 5: 11 x1 t04 06 cosine rule (2013)

Cosine RuleA

B C

h

a

bc

2 2 2h b x

2 2 2 2 22c b x a ax x

x

22 2c h a x

2 2 2b a ax

Page 6: 11 x1 t04 06 cosine rule (2013)

Cosine RuleA

B C

h

a

bc

2 2 2h b x

2 2 2 2 22c b x a ax x

x

22 2c h a x

2 2 2b a ax

But cos

cos

x Cbx b C

Page 7: 11 x1 t04 06 cosine rule (2013)

Cosine RuleA

B C

h

a

bc

2 2 2h b x

2 2 2 2 22c b x a ax x

x

22 2c h a x

2 2 2b a ax

But cos

cos

x Cbx b C

2 2 2 2 cosc b a ab C

Page 8: 11 x1 t04 06 cosine rule (2013)

Cosine RuleA

B C

h

a

bc

2 2 2h b x

2 2 2 2 22c b x a ax x

2 2 2

In any ABC2 cosa b c bc A

x

22 2c h a x

2 2 2b a ax

But cos

cos

x Cbx b C

2 2 2 2 cosc b a ab C

2 2 2 2 cosb a c ac B 2 2 2 2 cosc a b ab C

Page 9: 11 x1 t04 06 cosine rule (2013)

e.g. iTF

M

t

98 13

3

7

Page 10: 11 x1 t04 06 cosine rule (2013)

e.g. iTF

M

t

98 13

3

2 2 2 2 cost f m fm T 7 2 2 23 7 2 3 7 cos98 13t

Page 11: 11 x1 t04 06 cosine rule (2013)

e.g. iTF

M

t

98 13

3

2 2 2 2 cost f m fm T

8 units (to nearest whole number)t

7 2 2 23 7 2 3 7 cos98 13t

Page 12: 11 x1 t04 06 cosine rule (2013)

e.g. iTF

M

t

98 13

3

2 2 2 2 cost f m fm T

8 units (to nearest whole number)t

( )ii

F

A

S

20

6

7 2 2 23 7 2 3 7 cos98 13t

15

Page 13: 11 x1 t04 06 cosine rule (2013)

e.g. iTF

M

t

98 13

3

2 2 2 2 cost f m fm T

8 units (to nearest whole number)t

( )ii

F

A

S

20

6

2 2 2 2 cosf a s as F 2 2 2

cos2

a s fFas

7 2 2 23 7 2 3 7 cos98 13t

15

Page 14: 11 x1 t04 06 cosine rule (2013)

e.g. iTF

M

t

98 13

3

2 2 2 2 cost f m fm T

8 units (to nearest whole number)t

( )ii

F

A

S

20

6

2 2 2 2 cosf a s as F 2 2 2

cos2

a s fFas

7 2 2 23 7 2 3 7 cos98 13t

15

2 2 26 15 20cos2 6 15

F

Page 15: 11 x1 t04 06 cosine rule (2013)

e.g. iTF

M

t

98 13

3

2 2 2 2 cost f m fm T

8 units (to nearest whole number)t

( )ii

F

A

S

20

6

2 2 2 2 cosf a s as F 2 2 2

cos2

a s fFas

140 33F

7 2 2 23 7 2 3 7 cos98 13t

15

2 2 26 15 20cos2 6 15

F

Page 16: 11 x1 t04 06 cosine rule (2013)

iii

B

A

b

257

C3

Page 17: 11 x1 t04 06 cosine rule (2013)

iii

B

A

b

257

C3

2 2 2 2 cosa b c bc A

2 2 2

2

3 7 2 7 cos 25

9 49 14 cos 25

b b

b b

Page 18: 11 x1 t04 06 cosine rule (2013)

iii

B

A

b

257

C3

2 2 2 2 cosa b c bc A

2 2 2

2

3 7 2 7 cos 25

9 49 14 cos 25

b b

b b

2 14 cos 25 40 0b b

Page 19: 11 x1 t04 06 cosine rule (2013)

iii

B

A

b

257

C3

2 2 2 2 cosa b c bc A

2 2 2

2

3 7 2 7 cos 25

9 49 14 cos 25

b b

b b

2 14 cos 25 40 0b b

214cos 25 196cos 25 1602

b

Page 20: 11 x1 t04 06 cosine rule (2013)

iii

B

A

b

257

C3

2 2 2 2 cosa b c bc A

2 2 2

2

3 7 2 7 cos 25

9 49 14 cos 25

b b

b b

2 14 cos 25 40 0b b

214cos 25 196cos 25 1602

b

5.85 units or 6.85 units (to 2 dp)b b

Page 21: 11 x1 t04 06 cosine rule (2013)

Exercise 4I; 1a, 2b, 4, 5, 7, 9, 11, 12, 13, 14*

Exercise 4J; evens