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Popular Trigonometria >

100+60sin((7pi)/3 x)=100

Solução

100 + 60 sin (\frac{7 π}{3} x) = 100

Solução

x = \frac{6 n}{7}, x = \frac{3}{7} + \frac{6 n}{7}

+1

Graus

x = 0^{\circ} + 49.11066 \dots^{\circ} n, x = 24.55533 \dots^{\circ} + 49.11066 \dots^{\circ} n

Passos da solução

100 + 60 sin (\frac{7 π}{3} x) = 100

Subtrair

100

de ambos os lados

100 + 60 sin (\frac{7 π}{3} x) - 100 = 100 - 100

Simplificar

60 sin (\frac{7 π}{3} x) = 0

Dividir ambos os lados por

60

60 sin (\frac{7 π}{3} x) = 0

Dividir ambos os lados por

60

\frac{60 sin ( \frac{7 π}{3} x )}{60} = \frac{0}{60}

Simplificar

sin (\frac{7 π}{3} x) = 0

sin (\frac{7 π}{3} x) = 0

Soluções gerais para

sin (\frac{7 π}{3} 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}

\frac{7 π}{3} x = 0 + 2 πn, \frac{7 π}{3} x = π + 2 πn

\frac{7 π}{3} x = 0 + 2 πn, \frac{7 π}{3} x = π + 2 πn

Resolver

\frac{7 π}{3} x = 0 + 2 πn : x = \frac{6 n}{7}

\frac{7 π}{3} x = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{7 π}{3} x = 2 πn

Multiplicar ambos os lados por

3

\frac{7 π}{3} x = 2 πn

Multiplicar ambos os lados por

3

3 \cdot \frac{7 π}{3} x = 3 \cdot 2 πn

Simplificar

7 π x = 6 πn

7 π x = 6 πn

Dividir ambos os lados por

7 π

7 π x = 6 πn

Dividir ambos os lados por

7 π

\frac{7 π x}{7 π} = \frac{6 πn}{7 π}

Simplificar

x = \frac{6 n}{7}

x = \frac{6 n}{7}

Resolver

\frac{7 π}{3} x = π + 2 πn : x = \frac{3}{7} + \frac{6 n}{7}

\frac{7 π}{3} x = π + 2 πn

Multiplicar ambos os lados por

3

\frac{7 π}{3} x = π + 2 πn

Multiplicar ambos os lados por

3

3 \cdot \frac{7 π}{3} x = 3 π + 3 \cdot 2 πn

Simplificar

7 π x = 3 π + 6 πn

7 π x = 3 π + 6 πn

Dividir ambos os lados por

7 π

7 π x = 3 π + 6 πn

Dividir ambos os lados por

7 π

\frac{7 π x}{7 π} = \frac{3 π}{7 π} + \frac{6 πn}{7 π}

Simplificar

\frac{7 π x}{7 π} = \frac{3 π}{7 π} + \frac{6 πn}{7 π}

Simplificar

\frac{7 π x}{7 π} : x

\frac{7 π x}{7 π}

Dividir:

\frac{7}{7} = 1

= \frac{π x}{π}

Eliminar o fator comum:

π

= x

Simplificar

\frac{3 π}{7 π} + \frac{6 πn}{7 π} : \frac{3}{7} + \frac{6 n}{7}

\frac{3 π}{7 π} + \frac{6 πn}{7 π}

Cancelar

\frac{3 π}{7 π} : \frac{3}{7}

\frac{3 π}{7 π}

Eliminar o fator comum:

π

= \frac{3}{7}

= \frac{3}{7} + \frac{6 πn}{7 π}

Cancelar

\frac{6 πn}{7 π} : \frac{6 n}{7}

\frac{6 πn}{7 π}

Eliminar o fator comum:

π

= \frac{6 n}{7}

= \frac{3}{7} + \frac{6 n}{7}

x = \frac{3}{7} + \frac{6 n}{7}

x = \frac{3}{7} + \frac{6 n}{7}

x = \frac{3}{7} + \frac{6 n}{7}

x = \frac{6 n}{7}, x = \frac{3}{7} + \frac{6 n}{7}

Gráfico

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