Transcript
Page 1: 12 x1 t05 06 general solutions (2012)

General Solutions of Trig Equations

Page 2: 12 x1 t05 06 general solutions (2012)

General Solutions of Trig Equations

xsin

Page 3: 12 x1 t05 06 general solutions (2012)

General Solutions of Trig Equations

xsin0x

Page 4: 12 x1 t05 06 general solutions (2012)

General Solutions of Trig Equations

xsin0x

x1sinx1sin

Page 5: 12 x1 t05 06 general solutions (2012)

General Solutions of Trig Equations

xsin0x

x1sinx1sin

xx 11 sinor sin

Page 6: 12 x1 t05 06 general solutions (2012)

General Solutions of Trig Equations

xsin0x

x1sinx1sin

xx 11 sinor sin

0x

Page 7: 12 x1 t05 06 general solutions (2012)

General Solutions of Trig Equations

xsin0x

x1sinx1sin

xx 11 sinor sin

0x

x1sin x1sin

Page 8: 12 x1 t05 06 general solutions (2012)

General Solutions of Trig Equations

xsin0x

x1sinx1sin

xx 11 sinor sin

0x

x1sin x1sin

xx 11 sin2or sin

Page 9: 12 x1 t05 06 general solutions (2012)

General Solutions of Trig Equations

xsin0x

x1sinx1sin

xx 11 sinor sin

0x

x1sin x1sin

xx 11 sin2or sin xx 11 sin2or sin

Page 10: 12 x1 t05 06 general solutions (2012)

General Solutions of Trig Equations

xsin0x

x1sinx1sin

xx 11 sinor sin

0x

x1sin x1sin

xx 11 sin2or sin xx 11 sin2or sin

xsin xk k 1sin1 where k is an integer

Page 11: 12 x1 t05 06 general solutions (2012)

xcos

Page 12: 12 x1 t05 06 general solutions (2012)

xcos0x

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xcos0x

x1cos

x1cos

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xcos0x

x1cos

x1cos

xx 11 cos2or cos

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xcos0x

x1cos

x1cos

xx 11 cos2or cos

0x

Page 16: 12 x1 t05 06 general solutions (2012)

xcos0x

x1cos

x1cos

xx 11 cos2or cos

0x

x1cos x1cos

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xcos0x

x1cos

x1cos

xx 11 cos2or cos

0x

x1cos x1cos

xx 11 cosor cos

Page 18: 12 x1 t05 06 general solutions (2012)

xcos0x

x1cos

x1cos

xx 11 cos2or cos

0x

x1cos x1cos

xx 11 cosor cos

xx

xx11

11

cos2or coscosor cos

Page 19: 12 x1 t05 06 general solutions (2012)

xcos0x

x1cos

x1cos

xx 11 cos2or cos

0x

x1cos x1cos

xx 11 cosor cos

xx

xx11

11

cos2or coscosor cos

xcosxk 1cos2 where k is an integer

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xtan

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xtan0x

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xtan0x

x1tan

x1tan

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xtan0x

x1tan

x1tan

xx 11 tanor tan

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xtan0x

x1tan

x1tan

xx 11 tanor tan

0x

Page 25: 12 x1 t05 06 general solutions (2012)

xtan0x

x1tan

x1tan

xx 11 tanor tan

0x

x1tan x1tan

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xtan0x

x1tan

x1tan

xx 11 tanor tan

0x

x1tan x1tan

xx 11 tan2or tan

Page 27: 12 x1 t05 06 general solutions (2012)

xtan0x

x1tan

x1tan

xx 11 tanor tan

0x

x1tan x1tan

xx 11 tan2or tan

xx 11 tan2or tan

Page 28: 12 x1 t05 06 general solutions (2012)

xtan0x

x1tan

x1tan

xx 11 tanor tan

0x

x1tan x1tan

xx 11 tan2or tan

xx 11 tan2or tan

xtanxk 1tan where k is an integer

Page 29: 12 x1 t05 06 general solutions (2012)

23sin e.g. i

Page 30: 12 x1 t05 06 general solutions (2012)

23sin e.g. i

23sin1 1kk

where k is an integer

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23sin e.g. i

23sin1 1kk

where k is an integer

3

1 kk

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23sin e.g. i

23sin1 1kk

where k is an integer

3

1 kk

20If

32,

3

3,

3

Page 33: 12 x1 t05 06 general solutions (2012)

23sin e.g. i

23sin1 1kk

where k is an integer

3

1 kk

20If

32,

3

3,

3

2

1cos ii

Page 34: 12 x1 t05 06 general solutions (2012)

23sin e.g. i

23sin1 1kk

where k is an integer

3

1 kk

20If

32,

3

3,

3

2

1cos ii

21cos2 1k

where k is an integer

Page 35: 12 x1 t05 06 general solutions (2012)

23sin e.g. i

23sin1 1kk

where k is an integer

3

1 kk

20If

32,

3

3,

3

2

1cos ii

21cos2 1k

where k is an integer

432 k

Page 36: 12 x1 t05 06 general solutions (2012)

23sin e.g. i

23sin1 1kk

where k is an integer

3

1 kk

20If

32,

3

3,

3

2

1cos ii

21cos2 1k

where k is an integer

432 k

20If

45,

43

432,

43

Page 37: 12 x1 t05 06 general solutions (2012)

3

1tan iii

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3

1tan iii

31tan 1k

where k is an integer

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3

1tan iii

31tan 1k

where k is an integer

6 k

Page 40: 12 x1 t05 06 general solutions (2012)

3

1tan iii

31tan 1k

where k is an integer

6 k

20If

67,

6

6,

6

Page 41: 12 x1 t05 06 general solutions (2012)

3

1tan iii

31tan 1k

where k is an integer

6 k

20If

67,

6

6,

6

7

5sinsin iv

Page 42: 12 x1 t05 06 general solutions (2012)

3

1tan iii

31tan 1k

where k is an integer

6 k

20If

67,

6

6,

6

7

5sinsin iv

7

5sinsin1 1 kk

Page 43: 12 x1 t05 06 general solutions (2012)

3

1tan iii

31tan 1k

where k is an integer

6 k

20If

67,

6

6,

6

7

5sinsin iv

7

5sinsin1 1 kk

where k is an integer

7

21 kk

Page 44: 12 x1 t05 06 general solutions (2012)

3

1tan iii

31tan 1k

where k is an integer

6 k

20If

67,

6

6,

6

7

5sinsin iv

7

5sinsin1 1 kk

where k is an integer

7

21 kk

9

cos2cos xv

Page 45: 12 x1 t05 06 general solutions (2012)

3

1tan iii

31tan 1k

where k is an integer

6 k

20If

67,

6

6,

6

7

5sinsin iv

7

5sinsin1 1 kk

where k is an integer

7

21 kk

9

cos2cos xv

9coscos22 1 kx

Page 46: 12 x1 t05 06 general solutions (2012)

3

1tan iii

31tan 1k

where k is an integer

6 k

20If

67,

6

6,

6

7

5sinsin iv

7

5sinsin1 1 kk

where k is an integer

7

21 kk

9

cos2cos xv

9coscos22 1 kx

922 kx

Page 47: 12 x1 t05 06 general solutions (2012)

3

1tan iii

31tan 1k

where k is an integer

6 k

20If

67,

6

6,

6

7

5sinsin iv

7

5sinsin1 1 kk

where k is an integer

7

21 kk

9

cos2cos xv

9coscos22 1 kx

922 kx

18 kx

where k is an integer

Page 48: 12 x1 t05 06 general solutions (2012)

Exercise 1F; 4 to 8 ace etc9 to 1112ac


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