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3sin(x)tan(x)+sqrt(3)sin(x)=0

Solução

3 sin (x) tan (x) + 3 sin (x) = 0

x = 2 πn, x = π + 2 πn, x = \frac{5 π}{6} + πn

Graus

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n, x = 15 0^{\circ} + 18 0^{\circ} n

Passos da solução

3 sin (x) tan (x) + 3 sin (x) = 0

Fatorar

3 sin (x) tan (x) + 3 sin (x) : sin (x) (3 tan (x) + 3)

3 sin (x) tan (x) + 3 sin (x)

Fatorar o termo comum

sin (x)

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

sin (x) (3 tan (x) + 3) = 0

Resolver cada parte separadamente

sin (x) = 0 or 3 tan (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

3 tan (x) + 3 = 0 : x = \frac{5 π}{6} + πn

3 tan (x) + 3 = 0

Mova

3

para o lado direito

3 tan (x) + 3 = 0

Subtrair

3

de ambos os lados

3 tan (x) + 3 - 3 = 0 - 3

Simplificar

3 tan (x) = - 3

3 tan (x) = - 3

Dividir ambos os lados por

3

3 tan (x) = - 3

Dividir ambos os lados por

3

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

Simplificar

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

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

Soluções gerais para

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

tan (x)

tabela de periodicidade com ciclo de

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{5 π}{6} + πn

x = \frac{5 π}{6} + πn

Combinar toda as soluções

x = 2 πn, x = π + 2 πn, x = \frac{5 π}{6} + πn