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Popular Trigonometria >

sin(wpi)=0

Solução

sin (w π) = 0

Solução

w = 2 n, w = 1 + 2 n

+1

Graus

w = 0^{\circ} + 114.59155 \dots^{\circ} n, w = 57.29577 \dots^{\circ} + 114.59155 \dots^{\circ} n

Passos da solução

sin (w π) = 0

Soluções gerais para

sin (w π) = 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}

w π = 0 + 2 πn, w π = π + 2 πn

w π = 0 + 2 πn, w π = π + 2 πn

Resolver

w π = 0 + 2 πn : w = 2 n

w π = 0 + 2 πn

0 + 2 πn = 2 πn

w π = 2 πn

Dividir ambos os lados por

π

w π = 2 πn

Dividir ambos os lados por

π

\frac{w π}{π} = \frac{2 πn}{π}

Simplificar

w = 2 n

w = 2 n

Resolver

w π = π + 2 πn : w = 1 + 2 n

w π = π + 2 πn

Dividir ambos os lados por

π

w π = π + 2 πn

Dividir ambos os lados por

π

\frac{w π}{π} = \frac{π}{π} + \frac{2 πn}{π}

Simplificar

\frac{w π}{π} = \frac{π}{π} + \frac{2 πn}{π}

Simplificar

\frac{w π}{π} : w

\frac{w π}{π}

Eliminar o fator comum:

π

= w

Simplificar

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

\frac{π}{π} + \frac{2 πn}{π}

Aplicar a regra

\frac{a}{a} = 1

\frac{π}{π} = 1

= 1 + \frac{2 πn}{π}

Cancelar

\frac{2 πn}{π} : 2 n

\frac{2 πn}{π}

Eliminar o fator comum:

π

= 2 n

= 1 + 2 n

w = 1 + 2 n

w = 1 + 2 n

w = 1 + 2 n

w = 2 n, w = 1 + 2 n

Gráfico

Exemplos populares

cos (x) = - 8

2sin(2x)=sin^2(x)

2 sin (2 x) = sin^{2} (x)

sin^2(x)=-(1/2)

sin^{2} (x) = - (\frac{1}{2})

sin(x/2)-cos(x/2)=0

sin (\frac{x}{2}) - cos (\frac{x}{2}) = 0

2sin^2(x/3)=1,-pi<= ,x<= pi

2 sin^{2} (\frac{x}{3}) = 1, - π \leq, x \leq π