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Popular Trigonometria >

cos(pi+x)+cos(pi+x)=1

Solução

cos (π + x) + cos (π + x) = 1

Solução

x = \frac{π}{3} + 2 πn - π, x = \frac{5 π}{3} + 2 πn - π

+1

Graus

x = - 12 0^{\circ} + 36 0^{\circ} n, x = 12 0^{\circ} + 36 0^{\circ} n

Passos da solução

cos (π + x) + cos (π + x) = 1

Simplificar

cos (π + x) + cos (π + x) : 2 cos (π + x)

cos (π + x) + cos (π + x)

Somar elementos similares:

cos (x + π) + cos (x + π) = 2 cos (x + π)

= 2 cos (x + π)

2 cos (π + x) = 1

Dividir ambos os lados por

2

2 cos (π + x) = 1

Dividir ambos os lados por

2

\frac{2 cos ( π + x )}{2} = \frac{1}{2}

Simplificar

cos (π + x) = \frac{1}{2}

cos (π + x) = \frac{1}{2}

Soluções gerais para

cos (π + x) = \frac{1}{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}

π + x = \frac{π}{3} + 2 πn, π + x = \frac{5 π}{3} + 2 πn

π + x = \frac{π}{3} + 2 πn, π + x = \frac{5 π}{3} + 2 πn

Resolver

π + x = \frac{π}{3} + 2 πn : x = \frac{π}{3} + 2 πn - π

π + x = \frac{π}{3} + 2 πn

Mova

π

para o lado direito

π + x = \frac{π}{3} + 2 πn

Subtrair

π

de ambos os lados

π + x - π = \frac{π}{3} + 2 πn - π

Simplificar

x = \frac{π}{3} + 2 πn - π

x = \frac{π}{3} + 2 πn - π

Resolver

π + x = \frac{5 π}{3} + 2 πn : x = \frac{5 π}{3} + 2 πn - π

π + x = \frac{5 π}{3} + 2 πn

Mova

π

para o lado direito

π + x = \frac{5 π}{3} + 2 πn

Subtrair

π

de ambos os lados

π + x - π = \frac{5 π}{3} + 2 πn - π

Simplificar

x = \frac{5 π}{3} + 2 πn - π

x = \frac{5 π}{3} + 2 πn - π

x = \frac{π}{3} + 2 πn - π, x = \frac{5 π}{3} + 2 πn - π

Gráfico

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