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Popular Trigonometria >

sin(0.5pi)cos(0.5pi)=0.5sin(2x+1)

Solução

sin (0.5 π) cos (0.5 π) = 0.5 sin (2 x + 1)

Solução

x = πn - \frac{1}{2}, x = \frac{π}{2} - \frac{1}{2} + πn

Graus

x = - 28.64788 \dots^{\circ} + 18 0^{\circ} n, x = 61.35211 \dots^{\circ} + 18 0^{\circ} n

Passos da solução

sin (0.5 π) cos (0.5 π) = 0.5 sin (2 x + 1)

sin (0.5 π) = 1

sin (0.5 π)

= sin (\frac{1}{2} π)

Simplificar:

\frac{1}{2} π = \frac{π}{2}

\frac{1}{2} π

Multiplicar frações:

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

= \frac{1 π}{2}

Multiplicar:

1 π = π

= \frac{π}{2}

= sin (\frac{π}{2})

Utilizar a seguinte identidade trivial:

sin (\frac{π}{2}) = 1

sin (\frac{π}{2})

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}

= 1

= 1

cos (0.5 π) = 0

cos (0.5 π)

= cos (\frac{1}{2} π)

Simplificar:

\frac{1}{2} π = \frac{π}{2}

\frac{1}{2} π

Multiplicar frações:

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

= \frac{1 π}{2}

Multiplicar:

1 π = π

= \frac{π}{2}

= cos (\frac{π}{2})

Utilizar a seguinte identidade trivial:

cos (\frac{π}{2}) = 0

cos (\frac{π}{2})

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 0

= 0

1 \cdot 0 = 0.5 sin (2 x + 1)

Trocar lados

0.5 sin (2 x + 1) = 1 \cdot 0

Aplicar a regra

0 \cdot a = 0

0.5 sin (2 x + 1) = 0

Multiplicar ambos os lados por

10

0.5 sin (2 x + 1) = 0

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere is one digit to the right of the decimal point, therefore multiply by

10

0.5 sin (2 x + 1) \cdot 10 = 0 \cdot 10

Simplificar

5 sin (2 x + 1) = 0

5 sin (2 x + 1) = 0

Dividir ambos os lados por

5

5 sin (2 x + 1) = 0

Dividir ambos os lados por

5

\frac{5 sin ( 2 x + 1 )}{5} = \frac{0}{5}

Simplificar

sin (2 x + 1) = 0

sin (2 x + 1) = 0

Soluções gerais para

sin (2 x + 1) = 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}

2 x + 1 = 0 + 2 πn, 2 x + 1 = π + 2 πn

2 x + 1 = 0 + 2 πn, 2 x + 1 = π + 2 πn

Resolver

2 x + 1 = 0 + 2 πn : x = πn - \frac{1}{2}

2 x + 1 = 0 + 2 πn

0 + 2 πn = 2 πn

2 x + 1 = 2 πn

Mova

1

para o lado direito

2 x + 1 = 2 πn

Subtrair

1

de ambos os lados

2 x + 1 - 1 = 2 πn - 1

Simplificar

2 x = 2 πn - 1

2 x = 2 πn - 1

Dividir ambos os lados por

2

2 x = 2 πn - 1

Dividir ambos os lados por

2

\frac{2 x}{2} = \frac{2 πn}{2} - \frac{1}{2}

Simplificar

x = πn - \frac{1}{2}

x = πn - \frac{1}{2}

Resolver

2 x + 1 = π + 2 πn : x = \frac{π}{2} - \frac{1}{2} + πn

2 x + 1 = π + 2 πn

Mova

1

para o lado direito

2 x + 1 = π + 2 πn

Subtrair

1

de ambos os lados

2 x + 1 - 1 = π + 2 πn - 1

Simplificar

2 x = π + 2 πn - 1

2 x = π + 2 πn - 1

Dividir ambos os lados por

2

2 x = π + 2 πn - 1

Dividir ambos os lados por

2

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

Simplificar

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

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

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

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

Agrupar termos semelhantes

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

Dividir:

\frac{2}{2} = 1

= \frac{π}{2} - \frac{1}{2} + πn

x = \frac{π}{2} - \frac{1}{2} + πn

x = \frac{π}{2} - \frac{1}{2} + πn

x = \frac{π}{2} - \frac{1}{2} + πn

x = πn - \frac{1}{2}, x = \frac{π}{2} - \frac{1}{2} + πn

Gráfico

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