English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Trigonometria >

3sin(2x+30)=tan(2x+30)

Solução

3 sin (2 x + 30) = tan (2 x + 30)

Solução

x = πn - 15, x = \frac{π}{2} + πn - 15, x = \frac{1.23095 \dots}{2} + πn - 15, x = π - \frac{1.23095 \dots}{2} + πn - 15

Graus

x = - 859.43669 \dots^{\circ} + 18 0^{\circ} n, x = - 769.43669 \dots^{\circ} + 18 0^{\circ} n, x = - 824.17230 \dots^{\circ} + 18 0^{\circ} n, x = - 714.70108 \dots^{\circ} + 18 0^{\circ} n

Passos da solução

3 sin (2 x + 30) = tan (2 x + 30)

Subtrair

tan (2 x + 30)

de ambos os lados

3 sin (2 x + 30) - tan (2 x + 30) = 0

Expresar com seno, cosseno

- tan (30 + 2 x) + 3 sin (30 + 2 x)

Utilizar a Identidade Básica da Trigonometria:

tan (x) = \frac{sin ( x )}{cos ( x )}

= - \frac{sin ( 30 + 2 x )}{cos ( 30 + 2 x )} + 3 sin (30 + 2 x)

Simplificar

- \frac{sin ( 30 + 2 x )}{cos ( 30 + 2 x )} + 3 sin (30 + 2 x) : \frac{- sin ( 30 + 2 x ) + 3 sin ( 30 + 2 x ) cos ( 30 + 2 x )}{cos ( 30 + 2 x )}

- \frac{sin ( 30 + 2 x )}{cos ( 30 + 2 x )} + 3 sin (30 + 2 x)

Converter para fração:

3 sin (2 x + 30) = \frac{3 sin ( 30 + 2 x ) cos ( 30 + 2 x )}{cos ( 30 + 2 x )}

= - \frac{sin ( 30 + 2 x )}{cos ( 30 + 2 x )} + \frac{3 sin ( 30 + 2 x ) cos ( 30 + 2 x )}{cos ( 30 + 2 x )}

Já que os denominadores são iguais, combinar as frações:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- sin ( 30 + 2 x ) + 3 sin ( 30 + 2 x ) cos ( 30 + 2 x )}{cos ( 30 + 2 x )}

= \frac{- sin ( 30 + 2 x ) + 3 sin ( 30 + 2 x ) cos ( 30 + 2 x )}{cos ( 30 + 2 x )}

\frac{- sin ( 30 + 2 x ) + 3 cos ( 30 + 2 x ) sin ( 30 + 2 x )}{cos ( 30 + 2 x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

- sin (30 + 2 x) + 3 cos (30 + 2 x) sin (30 + 2 x) = 0

Fatorar

- sin (30 + 2 x) + 3 cos (30 + 2 x) sin (30 + 2 x) : sin (2 (x + 15)) (3 cos (2 (x + 15)) - 1)

- sin (30 + 2 x) + 3 cos (30 + 2 x) sin (30 + 2 x)

Fatorar o termo comum

sin (30 + 2 x)

= sin (30 + 2 x) (- 1 + 3 cos (30 + 2 x))

Fatorar

2 x + 30 : 2 (x + 15)

2 x + 30

Fatorar o termo comum

2 : 2 (x + 15)

2 x + 30

Reescrever

30

como

2 \cdot 15

= 2 x + 2 \cdot 15

Fatorar o termo comum

2

= 2 (x + 15)

= 2 (x + 15)

= sin (2 x + 30) (3 cos (2 (x + 15)) - 1)

Fatorar

2 x + 30 : 2 (x + 15)

2 x + 30

Fatorar o termo comum

2 : 2 (x + 15)

2 x + 30

Reescrever

30

como

2 \cdot 15

= 2 x + 2 \cdot 15

Fatorar o termo comum

2

= 2 (x + 15)

= 2 (x + 15)

= sin (2 (x + 15)) (3 cos (2 (x + 15)) - 1)

sin (2 (x + 15)) (3 cos (2 (x + 15)) - 1) = 0

Resolver cada parte separadamente

sin (2 (x + 15)) = 0 or 3 cos (2 (x + 15)) - 1 = 0

sin (2 (x + 15)) = 0 : x = πn - 15, x = \frac{π}{2} + πn - 15

sin (2 (x + 15)) = 0

Soluções gerais para

sin (2 (x + 15)) = 0

sin (x)

tabela de periodicidade com ciclo de

2 πn

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

2 (x + 15) = 0 + 2 πn, 2 (x + 15) = π + 2 πn

2 (x + 15) = 0 + 2 πn, 2 (x + 15) = π + 2 πn

Resolver

2 (x + 15) = 0 + 2 πn : x = πn - 15

2 (x + 15) = 0 + 2 πn

0 + 2 πn = 2 πn

2 (x + 15) = 2 πn

Dividir ambos os lados por

2

2 (x + 15) = 2 πn

Dividir ambos os lados por

2

\frac{2 ( x + 15 )}{2} = \frac{2 πn}{2}

Simplificar

x + 15 = πn

x + 15 = πn

Mova

15

para o lado direito

x + 15 = πn

Subtrair

15

de ambos os lados

x + 15 - 15 = πn - 15

Simplificar

x = πn - 15

x = πn - 15

Resolver

2 (x + 15) = π + 2 πn : x = \frac{π}{2} + πn - 15

2 (x + 15) = π + 2 πn

Dividir ambos os lados por

2

2 (x + 15) = π + 2 πn

Dividir ambos os lados por

2

\frac{2 ( x + 15 )}{2} = \frac{π}{2} + \frac{2 πn}{2}

Simplificar

x + 15 = \frac{π}{2} + πn

x + 15 = \frac{π}{2} + πn

Mova

15

para o lado direito

x + 15 = \frac{π}{2} + πn

Subtrair

15

de ambos os lados

x + 15 - 15 = \frac{π}{2} + πn - 15

Simplificar

x = \frac{π}{2} + πn - 15

x = \frac{π}{2} + πn - 15

x = πn - 15, x = \frac{π}{2} + πn - 15

3 cos (2 (x + 15)) - 1 = 0 : x = \frac{arccos ( \frac{1}{3} )}{2} + πn - 15, x = π - \frac{arccos ( \frac{1}{3} )}{2} + πn - 15

3 cos (2 (x + 15)) - 1 = 0

Mova

1

para o lado direito

3 cos (2 (x + 15)) - 1 = 0

Adicionar

1

a ambos os lados

3 cos (2 (x + 15)) - 1 + 1 = 0 + 1

Simplificar

3 cos (2 (x + 15)) = 1

3 cos (2 (x + 15)) = 1

Dividir ambos os lados por

3

3 cos (2 (x + 15)) = 1

Dividir ambos os lados por

3

\frac{3 cos ( 2 ( x + 15 ) )}{3} = \frac{1}{3}

Simplificar

cos (2 (x + 15)) = \frac{1}{3}

cos (2 (x + 15)) = \frac{1}{3}

Aplique as propriedades trigonométricas inversas

cos (2 (x + 15)) = \frac{1}{3}

Soluções gerais para

cos (2 (x + 15)) = \frac{1}{3}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

2 (x + 15) = arccos (\frac{1}{3}) + 2 πn, 2 (x + 15) = 2 π - arccos (\frac{1}{3}) + 2 πn

2 (x + 15) = arccos (\frac{1}{3}) + 2 πn, 2 (x + 15) = 2 π - arccos (\frac{1}{3}) + 2 πn

Resolver

2 (x + 15) = arccos (\frac{1}{3}) + 2 πn : x = \frac{arccos ( \frac{1}{3} )}{2} + πn - 15

2 (x + 15) = arccos (\frac{1}{3}) + 2 πn

Dividir ambos os lados por

2

2 (x + 15) = arccos (\frac{1}{3}) + 2 πn

Dividir ambos os lados por

2

\frac{2 ( x + 15 )}{2} = \frac{arccos ( \frac{1}{3} )}{2} + \frac{2 πn}{2}

Simplificar

x + 15 = \frac{arccos ( \frac{1}{3} )}{2} + πn

x + 15 = \frac{arccos ( \frac{1}{3} )}{2} + πn

Mova

15

para o lado direito

x + 15 = \frac{arccos ( \frac{1}{3} )}{2} + πn

Subtrair

15

de ambos os lados

x + 15 - 15 = \frac{arccos ( \frac{1}{3} )}{2} + πn - 15

Simplificar

x = \frac{arccos ( \frac{1}{3} )}{2} + πn - 15

x = \frac{arccos ( \frac{1}{3} )}{2} + πn - 15

Resolver

2 (x + 15) = 2 π - arccos (\frac{1}{3}) + 2 πn : x = π - \frac{arccos ( \frac{1}{3} )}{2} + πn - 15

2 (x + 15) = 2 π - arccos (\frac{1}{3}) + 2 πn

Dividir ambos os lados por

2

2 (x + 15) = 2 π - arccos (\frac{1}{3}) + 2 πn

Dividir ambos os lados por

2

\frac{2 ( x + 15 )}{2} = \frac{2 π}{2} - \frac{arccos ( \frac{1}{3} )}{2} + \frac{2 πn}{2}

Simplificar

x + 15 = π - \frac{arccos ( \frac{1}{3} )}{2} + πn

x + 15 = π - \frac{arccos ( \frac{1}{3} )}{2} + πn

Mova

15

para o lado direito

x + 15 = π - \frac{arccos ( \frac{1}{3} )}{2} + πn

Subtrair

15

de ambos os lados

x + 15 - 15 = π - \frac{arccos ( \frac{1}{3} )}{2} + πn - 15

Simplificar

x = π - \frac{arccos ( \frac{1}{3} )}{2} + πn - 15

x = π - \frac{arccos ( \frac{1}{3} )}{2} + πn - 15

x = \frac{arccos ( \frac{1}{3} )}{2} + πn - 15, x = π - \frac{arccos ( \frac{1}{3} )}{2} + πn - 15

Combinar toda as soluções

x = πn - 15, x = \frac{π}{2} + πn - 15, x = \frac{arccos ( \frac{1}{3} )}{2} + πn - 15, x = π - \frac{arccos ( \frac{1}{3} )}{2} + πn - 15

Mostrar soluções na forma decimal

x = πn - 15, x = \frac{π}{2} + πn - 15, x = \frac{1.23095 \dots}{2} + πn - 15, x = π - \frac{1.23095 \dots}{2} + πn - 15

Gráfico

Exemplos populares

16sin(t)cos(t)=4sin(t)

16 sin (t) cos (t) = 4 sin (t)

4cos(x)=4-4cos(x)

4 cos (x) = 4 - 4 cos (x)

cos(2x)-cos(6x)-sin(4x)=0,0<= x<= pi

cos (2 x) - cos (6 x) - sin (4 x) = 0, 0 \leq x \leq π

0=3sin(θ)

0 = 3 sin (θ)

2cos^2(x)+sin(x)-1=0,(0,2pi)

2 cos^{2} (x) + sin (x) - 1 = 0, (0, 2 π)