Solving a Trigonometric Equation Find the general solution of the equation.

Solving a Trigonometric EquationFind the general solution of the equation.

1cos2 .1 2 x2 2

x2cos2

1

xcos2

2

2

2cos 1x

4

x

4

4

4

4

3,

4

x

2

n

4

4


29tan 7 .2 x

7 7xtan 1

1tan 1 x

4

3x

4

4

4

7,

4

3x n

4

7tan 7 x

42


21cot .3 2 xx2cot 3

xcot 3

3

3tan 1x

6

x

6

6

6

6

5,

6

x n

6

6

xtan3

3

6

5,

n


3 cos2 .4 x2 2

xcos2

3

2

3cos 1x

6

x

6

62

6

11,

6

x n2

6

6

11,

n2


01 cot .5 x

xtan 1 1tan 1 x

4

3x

4

4

4

7,

4

3x n

4

1cot x

42


034sin .6 2 xx2sin4 3

xsin2

3

2

3sin 1x

3

x

3

3

3

3

2,

3

x n

3

3

3

2,

n4 4

x2sin4

3

Factoring to Solve a Trigonometric EquationSolve the equation in the interval 0 < x < 2.

0sinsin .7 2 xx 0 sin x xsin

0sin x 1sin x0x

1

,2

x


xxx cossin2sin 3 .8

0 sin x 3

0sin x

3cos2 x

0x

xcos2

,6

x

0cossin2sin 3 xxx

2

3cos x

6

11,

6

62

6


01sin1cos .9 xx

1cos x

0x2

x

1sin x


xxx tan2sectan .10

0 tan x xsec

0tan x

2sec x

0x

2

,4

x

0tan2sectan xxx

2

2cos x

4

7,

4

42

4


xxx sintansin .11

0 sin x xtan

0sin x

0x

1

,4

x

0sintansin xxx

1tan x

4

5,

4

4

4


0tantan .12 2 xx 0 tan x 1

0tan x

0x

xtan

,4

3x

1tan x

4

7,

4

4

4

42

Using the Quadratic FormulaSolve the equation in the interval 0 < x < .

03sinsin2 .13 2 xx 0 xsin2

3sin2 x 1sin x3

2

x

xsin 1

2

3sin x


01tan3tan2 .14 2 xx

tan x 3 9 4 2 14

4

93tan

x 8

4

173

781.1281.0

781.1tan 1x06.1x

281.0tan 1 x

87.2x274.0

274.0


2cos3cos5 .15 2 xx

cos x 3 9 4 5 2

10

10

93cos

x 40

10

493

4.01

4.0cos 1x16.1x

1cos 1 xx

02cos3cos5 2 xx


2cos4cos .16 2 xx

cos x 4 16 4 1 2

2

2

614cos

x

82

84

414.3586.0

586.0cos 1x945.0x

02cos4cos2 xx

Solving a Trigonometric Equation Find the general solution of the equation.

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