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Popular Trigonometria >

120=120sin(pi/3 c)

Solução

120 = 120 sin (\frac{π}{3} c)

Solução

c = \frac{3}{2} + 6 n

+1

Graus

c = 85.94366 \dots^{\circ} + 343.77467 \dots^{\circ} n

Passos da solução

120 = 120 sin (\frac{π}{3} c)

Trocar lados

120 sin (\frac{π}{3} c) = 120

Dividir ambos os lados por

120

120 sin (\frac{π}{3} c) = 120

Dividir ambos os lados por

120

\frac{120 sin ( \frac{π}{3} c )}{120} = \frac{120}{120}

Simplificar

sin (\frac{π}{3} c) = 1

sin (\frac{π}{3} c) = 1

Soluções gerais para

sin (\frac{π}{3} c) = 1

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{π}{3} c = \frac{π}{2} + 2 πn

\frac{π}{3} c = \frac{π}{2} + 2 πn

Resolver

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

\frac{π}{3} c = \frac{π}{2} + 2 πn

Multiplicar ambos os lados por

3

\frac{π}{3} c = \frac{π}{2} + 2 πn

Multiplicar ambos os lados por

3

3 \cdot \frac{π}{3} c = 3 \cdot \frac{π}{2} + 3 \cdot 2 πn

Simplificar

3 \cdot \frac{π}{3} c = 3 \cdot \frac{π}{2} + 3 \cdot 2 πn

Simplificar

3 \cdot \frac{π}{3} c : π c

3 \cdot \frac{π}{3} c

Multiplicar frações:

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

= \frac{3 π}{3} c

Eliminar o fator comum:

3

= c π

Simplificar

3 \cdot \frac{π}{2} + 3 \cdot 2 πn : \frac{3 π}{2} + 6 πn

3 \cdot \frac{π}{2} + 3 \cdot 2 πn

Multiplicar

3 \cdot \frac{π}{2} : \frac{3 π}{2}

3 \cdot \frac{π}{2}

Multiplicar frações:

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

= \frac{π 3}{2}

= \frac{3 π}{2} + 3 \cdot 2 πn

Multiplicar os números:

3 \cdot 2 = 6

= \frac{3 π}{2} + 6 πn

π c = \frac{3 π}{2} + 6 πn

π c = \frac{3 π}{2} + 6 πn

π c = \frac{3 π}{2} + 6 πn

Dividir ambos os lados por

π

π c = \frac{3 π}{2} + 6 πn

Dividir ambos os lados por

π

\frac{π c}{π} = \frac{\frac{3 π}{2}}{π} + \frac{6 πn}{π}

Simplificar

\frac{π c}{π} = \frac{\frac{3 π}{2}}{π} + \frac{6 πn}{π}

Simplificar

\frac{π c}{π} : c

\frac{π c}{π}

Eliminar o fator comum:

π

= c

Simplificar

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

\frac{\frac{3 π}{2}}{π} + \frac{6 πn}{π}

\frac{\frac{3 π}{2}}{π} = \frac{3}{2}

\frac{\frac{3 π}{2}}{π}

Aplicar as propriedades das frações:

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

= \frac{3 π}{2 π}

Eliminar o fator comum:

π

= \frac{3}{2}

\frac{6 πn}{π} = 6 n

\frac{6 πn}{π}

Eliminar o fator comum:

π

= 6 n

= \frac{3}{2} + 6 n

c = \frac{3}{2} + 6 n

c = \frac{3}{2} + 6 n

c = \frac{3}{2} + 6 n

c = \frac{3}{2} + 6 n

Gráfico

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