English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Trigonometria >

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

Solução

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

Solução

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

Graus

x = 0^{\circ} + 18 0^{\circ} n, x = 9 0^{\circ} + 18 0^{\circ} n, x = 35.26438 \dots^{\circ} + 18 0^{\circ} n, x = 144.73561 \dots^{\circ} + 18 0^{\circ} n

Passos da solução

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

Subtrair

3 sin (2 x)

de ambos os lados

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

Expresar com seno, cosseno

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

Utilizar a Identidade Básica da Trigonometria:

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

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

Simplificar

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

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

Converter para fração:

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

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

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

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

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

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

Fatorar

sin (2 x) - 3 cos (2 x) sin (2 x) : - sin (2 x) (3 cos (2 x) - 1)

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

Fatorar o termo comum

- sin (2 x)

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

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

Resolver cada parte separadamente

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

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

sin (2 x) = 0

Soluções gerais para

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

2 x = 0 + 2 πn, 2 x = π + 2 πn

Resolver

2 x = 0 + 2 πn : x = πn

2 x = 0 + 2 πn

0 + 2 πn = 2 πn

2 x = 2 πn

Dividir ambos os lados por

2

2 x = 2 πn

Dividir ambos os lados por

2

\frac{2 x}{2} = \frac{2 πn}{2}

Simplificar

x = πn

x = πn

Resolver

2 x = π + 2 πn : x = \frac{π}{2} + πn

2 x = π + 2 πn

Dividir ambos os lados por

2

2 x = π + 2 πn

Dividir ambos os lados por

2

\frac{2 x}{2} = \frac{π}{2} + \frac{2 πn}{2}

Simplificar

x = \frac{π}{2} + πn

x = \frac{π}{2} + πn

x = πn, x = \frac{π}{2} + πn

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

3 cos (2 x) - 1 = 0

Mova

1

para o lado direito

3 cos (2 x) - 1 = 0

Adicionar

1

a ambos os lados

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

Simplificar

3 cos (2 x) = 1

3 cos (2 x) = 1

Dividir ambos os lados por

3

3 cos (2 x) = 1

Dividir ambos os lados por

3

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

Simplificar

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

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

Aplique as propriedades trigonométricas inversas

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

Soluções gerais para

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

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

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

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

Resolver

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

2 x = arccos (\frac{1}{3}) + 2 πn

Dividir ambos os lados por

2

2 x = arccos (\frac{1}{3}) + 2 πn

Dividir ambos os lados por

2

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

Simplificar

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

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

Resolver

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

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

Dividir ambos os lados por

2

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

Dividir ambos os lados por

2

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

Simplificar

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

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

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

Combinar toda as soluções

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

Mostrar soluções na forma decimal

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

Gráfico

Exemplos populares

4sin(x)+1=2sin(x)

4 sin (x) + 1 = 2 sin (x)

(sin(2x))/(cos(x))=1

\frac{sin ( 2 x )}{cos ( x )} = 1

tan^2(x)+4tan(x)+1=0

tan^{2} (x) + 4 tan (x) + 1 = 0

2cosh^2(x)-5sinh(x)=5

2 cosh^{2} (x) - 5 sinh (x) = 5

10+5cos(2x)=15cos(x)

10 + 5 cos (2 x) = 15 cos (x)