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Popular Trigonometria >

sin(2p+1)=-1

Solução

sin (2 p + 1) = - 1

Solução

p = πn - \frac{1}{2} + \frac{3 π}{4}

+1

Graus

p = 106.35211 \dots^{\circ} + 18 0^{\circ} n

Passos da solução

sin (2 p + 1) = - 1

Soluções gerais para

sin (2 p + 1) = - 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}

2 p + 1 = \frac{3 π}{2} + 2 πn

2 p + 1 = \frac{3 π}{2} + 2 πn

Resolver

2 p + 1 = \frac{3 π}{2} + 2 πn : p = πn - \frac{1}{2} + \frac{3 π}{4}

2 p + 1 = \frac{3 π}{2} + 2 πn

Mova

1

para o lado direito

2 p + 1 = \frac{3 π}{2} + 2 πn

Subtrair

1

de ambos os lados

2 p + 1 - 1 = \frac{3 π}{2} + 2 πn - 1

Simplificar

2 p = \frac{3 π}{2} + 2 πn - 1

2 p = \frac{3 π}{2} + 2 πn - 1

Dividir ambos os lados por

2

2 p = \frac{3 π}{2} + 2 πn - 1

Dividir ambos os lados por

2

\frac{2 p}{2} = \frac{\frac{3 π}{2}}{2} + \frac{2 πn}{2} - \frac{1}{2}

Simplificar

\frac{2 p}{2} = \frac{\frac{3 π}{2}}{2} + \frac{2 πn}{2} - \frac{1}{2}

Simplificar

\frac{2 p}{2} : p

\frac{2 p}{2}

Dividir:

\frac{2}{2} = 1

= p

Simplificar

\frac{\frac{3 π}{2}}{2} + \frac{2 πn}{2} - \frac{1}{2} : πn - \frac{1}{2} + \frac{3 π}{4}

\frac{\frac{3 π}{2}}{2} + \frac{2 πn}{2} - \frac{1}{2}

Agrupar termos semelhantes

= - \frac{1}{2} + \frac{2 πn}{2} + \frac{\frac{3 π}{2}}{2}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Dividir:

\frac{2}{2} = 1

= πn

\frac{\frac{3 π}{2}}{2} = \frac{3 π}{4}

\frac{\frac{3 π}{2}}{2}

Aplicar as propriedades das frações:

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

= \frac{3 π}{2 \cdot 2}

Multiplicar os números:

2 \cdot 2 = 4

= \frac{3 π}{4}

= - \frac{1}{2} + πn + \frac{3 π}{4}

Agrupar termos semelhantes

= πn - \frac{1}{2} + \frac{3 π}{4}

p = πn - \frac{1}{2} + \frac{3 π}{4}

p = πn - \frac{1}{2} + \frac{3 π}{4}

p = πn - \frac{1}{2} + \frac{3 π}{4}

p = πn - \frac{1}{2} + \frac{3 π}{4}

Gráfico

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