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Popular Trigonometria >

0=(110cos(377t))/8

Solução

0 = \frac{110 cos ( 377 t )}{8}

Solução

t = \frac{π}{754} + \frac{2 πn}{377}, t = \frac{3 π}{754} + \frac{2 πn}{377}

Graus

t = 0.23872 \dots^{\circ} + 0.95490 \dots^{\circ} n, t = 0.71618 \dots^{\circ} + 0.95490 \dots^{\circ} n

Passos da solução

0 = \frac{110 cos ( 377 t )}{8}

Trocar lados

\frac{110 cos ( 377 t )}{8} = 0

Multiplicar ambos os lados por

8

\frac{110 cos ( 377 t )}{8} = 0

Multiplicar ambos os lados por

8

\frac{8 \cdot 110 cos ( 377 t )}{8} = 0 \cdot 8

Simplificar

110 cos (377 t) = 0

110 cos (377 t) = 0

Dividir ambos os lados por

110

110 cos (377 t) = 0

Dividir ambos os lados por

110

\frac{110 cos ( 377 t )}{110} = \frac{0}{110}

Simplificar

cos (377 t) = 0

cos (377 t) = 0

Soluções gerais para

cos (377 t) = 0

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}

377 t = \frac{π}{2} + 2 πn, 377 t = \frac{3 π}{2} + 2 πn

377 t = \frac{π}{2} + 2 πn, 377 t = \frac{3 π}{2} + 2 πn

Resolver

377 t = \frac{π}{2} + 2 πn : t = \frac{π}{754} + \frac{2 πn}{377}

377 t = \frac{π}{2} + 2 πn

Dividir ambos os lados por

377

377 t = \frac{π}{2} + 2 πn

Dividir ambos os lados por

377

\frac{377 t}{377} = \frac{\frac{π}{2}}{377} + \frac{2 πn}{377}

Simplificar

\frac{377 t}{377} = \frac{\frac{π}{2}}{377} + \frac{2 πn}{377}

Simplificar

\frac{377 t}{377} : t

\frac{377 t}{377}

Dividir:

\frac{377}{377} = 1

= t

Simplificar

\frac{\frac{π}{2}}{377} + \frac{2 πn}{377} : \frac{π}{754} + \frac{2 πn}{377}

\frac{\frac{π}{2}}{377} + \frac{2 πn}{377}

\frac{\frac{π}{2}}{377} = \frac{π}{754}

\frac{\frac{π}{2}}{377}

Aplicar as propriedades das frações:

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

= \frac{π}{2 \cdot 377}

Multiplicar os números:

2 \cdot 377 = 754

= \frac{π}{754}

= \frac{π}{754} + \frac{2 πn}{377}

t = \frac{π}{754} + \frac{2 πn}{377}

t = \frac{π}{754} + \frac{2 πn}{377}

t = \frac{π}{754} + \frac{2 πn}{377}

Resolver

377 t = \frac{3 π}{2} + 2 πn : t = \frac{3 π}{754} + \frac{2 πn}{377}

377 t = \frac{3 π}{2} + 2 πn

Dividir ambos os lados por

377

377 t = \frac{3 π}{2} + 2 πn

Dividir ambos os lados por

377

\frac{377 t}{377} = \frac{\frac{3 π}{2}}{377} + \frac{2 πn}{377}

Simplificar

\frac{377 t}{377} = \frac{\frac{3 π}{2}}{377} + \frac{2 πn}{377}

Simplificar

\frac{377 t}{377} : t

\frac{377 t}{377}

Dividir:

\frac{377}{377} = 1

= t

Simplificar

\frac{\frac{3 π}{2}}{377} + \frac{2 πn}{377} : \frac{3 π}{754} + \frac{2 πn}{377}

\frac{\frac{3 π}{2}}{377} + \frac{2 πn}{377}

\frac{\frac{3 π}{2}}{377} = \frac{3 π}{754}

\frac{\frac{3 π}{2}}{377}

Aplicar as propriedades das frações:

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

= \frac{3 π}{2 \cdot 377}

Multiplicar os números:

2 \cdot 377 = 754

= \frac{3 π}{754}

= \frac{3 π}{754} + \frac{2 πn}{377}

t = \frac{3 π}{754} + \frac{2 πn}{377}

t = \frac{3 π}{754} + \frac{2 πn}{377}

t = \frac{3 π}{754} + \frac{2 πn}{377}

t = \frac{π}{754} + \frac{2 πn}{377}, t = \frac{3 π}{754} + \frac{2 πn}{377}

Gráfico

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