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Popular Trigonometria >

tan(x)= 5/3 sin(x)[0.2pi]

Solução

tan (x) = \frac{5}{3} sin (x) [0.2 π]

Solução

x = 2 πn, x = π + 2 πn, x = 0.30137 \dots + 2 πn, x = 2 π - 0.30137 \dots + 2 πn

Graus

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n, x = 17.26743 \dots^{\circ} + 36 0^{\circ} n, x = 342.73256 \dots^{\circ} + 36 0^{\circ} n

Passos da solução

tan (x) = \frac{5}{3} sin (x) [0.2 π]

Subtrair

\frac{5}{3} sin (x) [0.2 π]

de ambos os lados

tan (x) - \frac{π}{3} sin (x) = 0

Simplificar

tan (x) - \frac{π}{3} sin (x) : \frac{3 tan ( x ) - π sin ( x )}{3}

tan (x) - \frac{π}{3} sin (x)

Multiplicar

\frac{π}{3} sin (x) : \frac{π sin ( x )}{3}

\frac{π}{3} sin (x)

Multiplicar frações:

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

= \frac{π sin ( x )}{3}

= tan (x) - \frac{π sin ( x )}{3}

Converter para fração:

tan (x) = \frac{tan ( x ) 3}{3}

= \frac{tan ( x ) \cdot 3}{3} - \frac{π sin ( x )}{3}

Já que os denominadores são iguais, combinar as frações:

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

= \frac{tan ( x ) \cdot 3 - π sin ( x )}{3}

\frac{3 tan ( x ) - π sin ( x )}{3} = 0

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

3 tan (x) - π sin (x) = 0

Expresar com seno, cosseno

3 tan (x) - sin (x) π

Utilizar a Identidade Básica da Trigonometria:

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

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

Simplificar

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

3 \cdot \frac{sin ( x )}{cos ( x )} - sin (x) π

Multiplicar

3 \cdot \frac{sin ( x )}{cos ( x )} : \frac{3 sin ( x )}{cos ( x )}

3 \cdot \frac{sin ( x )}{cos ( x )}

Multiplicar frações:

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

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

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

Converter para fração:

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

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

Já que os denominadores são iguais, combinar as frações:

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

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

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

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

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

3 sin (x) - cos (x) sin (x) π = 0

Fatorar

3 sin (x) - cos (x) sin (x) π : - sin (x) (π cos (x) - 3)

3 sin (x) - cos (x) sin (x) π

Fatorar o termo comum

- sin (x)

= - sin (x) (- 3 + π cos (x))

- sin (x) (π cos (x) - 3) = 0

Resolver cada parte separadamente

sin (x) = 0 or π cos (x) - 3 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = 0

Soluções gerais para

sin (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}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

Resolver

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

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

π cos (x) - 3 = 0

Mova

3

para o lado direito

π cos (x) - 3 = 0

Adicionar

3

a ambos os lados

π cos (x) - 3 + 3 = 0 + 3

Simplificar

π cos (x) = 3

π cos (x) = 3

Dividir ambos os lados por

π

π cos (x) = 3

Dividir ambos os lados por

π

\frac{π cos ( x )}{π} = \frac{3}{π}

Simplificar

cos (x) = \frac{3}{π}

cos (x) = \frac{3}{π}

Aplique as propriedades trigonométricas inversas

cos (x) = \frac{3}{π}

Soluções gerais para

cos (x) = \frac{3}{π}

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

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

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

Combinar toda as soluções

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

Mostrar soluções na forma decimal

x = 2 πn, x = π + 2 πn, x = 0.30137 \dots + 2 πn, x = 2 π - 0.30137 \dots + 2 πn

Gráfico

Exemplos populares

4sin^2(x)-cos^2(x)=0

cos(pi/2-x)=cos(pi/2)-cos(x)

-3cos(pi/2-θ)=tan(θ)

3tan^2(x/3)=1

0.3=sin(9x)