General Solutions of Trig Equations

General Solutions of Trig Equations

xsin

General Solutions of Trig Equations

xsin0x

General Solutions of Trig Equations

xsin0x

x1sinx1sin

General Solutions of Trig Equations

xsin0x

x1sinx1sin

xx 11 sinor sin

General Solutions of Trig Equations

xsin0x

x1sinx1sin

xx 11 sinor sin

0x

General Solutions of Trig Equations

xsin0x

x1sinx1sin

xx 11 sinor sin

0x

x1sin x1sin

General Solutions of Trig Equations

xsin0x

x1sinx1sin

xx 11 sinor sin

0x

x1sin x1sin

xx 11 sin2or sin

General Solutions of Trig Equations

xsin0x

x1sinx1sin

xx 11 sinor sin

0x

x1sin x1sin

xx 11 sin2or sin xx 11 sin2or sin

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

xcos

xcos0x

xcos0x

x1cos

x1cos

xcos0x

x1cos

x1cos

xx 11 cos2or cos

xcos0x

x1cos

x1cos

xx 11 cos2or cos

0x

xcos0x

x1cos

x1cos

xx 11 cos2or cos

0x

x1cos x1cos

xcos0x

x1cos

x1cos

xx 11 cos2or cos

0x

x1cos x1cos

xx 11 cosor cos

xcos0x

x1cos

x1cos

xx 11 cos2or cos

0x

x1cos x1cos

xx 11 cosor cos

xx

xx11

11

cos2or coscosor cos

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

xtan

xtan0x

xtan0x

x1tan

x1tan

xtan0x

x1tan

x1tan

xx 11 tanor tan

xtan0x

x1tan

x1tan

xx 11 tanor tan

0x

xtan0x

x1tan

x1tan

xx 11 tanor tan

0x

x1tan x1tan

xtan0x

x1tan

x1tan

xx 11 tanor tan

0x

x1tan x1tan

xx 11 tan2or tan

xtan0x

x1tan

x1tan

xx 11 tanor tan

0x

x1tan x1tan

xx 11 tan2or tan

xx 11 tan2or tan

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

23sin e.g. i

23sin e.g. i

23sin1 1kk

where k is an integer

23sin e.g. i

23sin1 1kk

where k is an integer

3

1 kk

23sin e.g. i

23sin1 1kk

where k is an integer

3

1 kk

20If

32,

3

3,

3

23sin e.g. i

23sin1 1kk

where k is an integer

3

1 kk

20If

32,

3

3,

3

2

1cos ii

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

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

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

3

1tan iii

3

1tan iii

31tan 1k

where k is an integer

3

1tan iii

31tan 1k

where k is an integer

6 k

3

1tan iii

31tan 1k

where k is an integer

6 k

20If

67,

6

6,

6

3

1tan iii

31tan 1k

where k is an integer

6 k

20If

67,

6

6,

6

7

5sinsin iv

3

1tan iii

31tan 1k

where k is an integer

6 k

20If

67,

6

6,

6

7

5sinsin iv

7

5sinsin1 1 kk

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

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

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

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

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

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