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Popular Trigonometria >

0.2=cos(2pit)

Solução

0.2 = cos (2 π t)

Solução

t = \frac{1.36943 \dots}{2 π} + n, t = 1 - \frac{1.36943 \dots}{2 π} + n

+1

Graus

t = 12.48778 \dots^{\circ}, t = 44.80799 \dots^{\circ}

Passos da solução

0.2 = cos (2 π t)

Trocar lados

cos (2 π t) = 0.2

Aplique as propriedades trigonométricas inversas

cos (2 π t) = 0.2

Soluções gerais para

cos (2 π t) = 0.2

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

2 π t = arccos (0.2) + 2 πn, 2 π t = 2 π - arccos (0.2) + 2 πn

2 π t = arccos (0.2) + 2 πn, 2 π t = 2 π - arccos (0.2) + 2 πn

Resolver

2 π t = arccos (0.2) + 2 πn : t = \frac{arccos ( 0.2 )}{2 π} + n

2 π t = arccos (0.2) + 2 πn

Dividir ambos os lados por

2 π

2 π t = arccos (0.2) + 2 πn

Dividir ambos os lados por

2 π

\frac{2 π t}{2 π} = \frac{arccos ( 0.2 )}{2 π} + \frac{2 πn}{2 π}

Simplificar

\frac{2 π t}{2 π} = \frac{arccos ( 0.2 )}{2 π} + \frac{2 πn}{2 π}

Simplificar

\frac{2 π t}{2 π} : t

\frac{2 π t}{2 π}

Dividir:

\frac{2}{2} = 1

= \frac{π t}{π}

Eliminar o fator comum:

π

= t

Simplificar

\frac{arccos ( 0.2 )}{2 π} + \frac{2 πn}{2 π} : \frac{arccos ( 0.2 )}{2 π} + n

\frac{arccos ( 0.2 )}{2 π} + \frac{2 πn}{2 π}

Cancelar

\frac{2 πn}{2 π} : n

\frac{2 πn}{2 π}

Cancelar

\frac{2 πn}{2 π} : n

\frac{2 πn}{2 π}

Dividir:

\frac{2}{2} = 1

= \frac{πn}{π}

Eliminar o fator comum:

π

= n

= n

= \frac{arccos ( 0.2 )}{2 π} + n

t = \frac{arccos ( 0.2 )}{2 π} + n

t = \frac{arccos ( 0.2 )}{2 π} + n

t = \frac{arccos ( 0.2 )}{2 π} + n

Resolver

2 π t = 2 π - arccos (0.2) + 2 πn : t = 1 - \frac{arccos ( 0.2 )}{2 π} + n

2 π t = 2 π - arccos (0.2) + 2 πn

Dividir ambos os lados por

2 π

2 π t = 2 π - arccos (0.2) + 2 πn

Dividir ambos os lados por

2 π

\frac{2 π t}{2 π} = \frac{2 π}{2 π} - \frac{arccos ( 0.2 )}{2 π} + \frac{2 πn}{2 π}

Simplificar

\frac{2 π t}{2 π} = \frac{2 π}{2 π} - \frac{arccos ( 0.2 )}{2 π} + \frac{2 πn}{2 π}

Simplificar

\frac{2 π t}{2 π} : t

\frac{2 π t}{2 π}

Dividir:

\frac{2}{2} = 1

= \frac{π t}{π}

Eliminar o fator comum:

π

= t

Simplificar

\frac{2 π}{2 π} - \frac{arccos ( 0.2 )}{2 π} + \frac{2 πn}{2 π} : 1 - \frac{arccos ( 0.2 )}{2 π} + n

\frac{2 π}{2 π} - \frac{arccos ( 0.2 )}{2 π} + \frac{2 πn}{2 π}

Aplicar a regra

\frac{a}{a} = 1

\frac{2 π}{2 π} = 1

= 1 - \frac{arccos ( 0.2 )}{2 π} + \frac{2 πn}{2 π}

Cancelar

\frac{2 πn}{2 π} : n

\frac{2 πn}{2 π}

Cancelar

\frac{2 πn}{2 π} : n

\frac{2 πn}{2 π}

Dividir:

\frac{2}{2} = 1

= \frac{πn}{π}

Eliminar o fator comum:

π

= n

= n

= 1 - \frac{arccos ( 0.2 )}{2 π} + n

t = 1 - \frac{arccos ( 0.2 )}{2 π} + n

t = 1 - \frac{arccos ( 0.2 )}{2 π} + n

t = 1 - \frac{arccos ( 0.2 )}{2 π} + n

t = \frac{arccos ( 0.2 )}{2 π} + n, t = 1 - \frac{arccos ( 0.2 )}{2 π} + n

Mostrar soluções na forma decimal

t = \frac{1.36943 \dots}{2 π} + n, t = 1 - \frac{1.36943 \dots}{2 π} + n

Gráfico

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