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Popular >

cos(2x)-0.25=0

Solução

cos (2 x) - 0.25 = 0

Solução

x = \frac{1.31811 \dots}{2} + πn, x = π - \frac{1.31811 \dots}{2} + πn

+1

Graus

x = 37.76124 \dots^{\circ} + 18 0^{\circ} n, x = 142.23875 \dots^{\circ} + 18 0^{\circ} n

Passos da solução

cos (2 x) - 0.25 = 0

Mova

0.25

para o lado direito

cos (2 x) - 0.25 = 0

Adicionar

0.25

a ambos os lados

cos (2 x) - 0.25 + 0.25 = 0 + 0.25

Simplificar

cos (2 x) = 0.25

cos (2 x) = 0.25

Aplique as propriedades trigonométricas inversas

cos (2 x) = 0.25

Soluções gerais para

cos (2 x) = 0.25

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

2 x = arccos (0.25) + 2 πn, 2 x = 2 π - arccos (0.25) + 2 πn

2 x = arccos (0.25) + 2 πn, 2 x = 2 π - arccos (0.25) + 2 πn

Resolver

2 x = arccos (0.25) + 2 πn : x = \frac{arccos ( 0.25 )}{2} + πn

2 x = arccos (0.25) + 2 πn

Dividir ambos os lados por

2

2 x = arccos (0.25) + 2 πn

Dividir ambos os lados por

2

\frac{2 x}{2} = \frac{arccos ( 0.25 )}{2} + \frac{2 πn}{2}

Simplificar

x = \frac{arccos ( 0.25 )}{2} + πn

x = \frac{arccos ( 0.25 )}{2} + πn

Resolver

2 x = 2 π - arccos (0.25) + 2 πn : x = π - \frac{arccos ( 0.25 )}{2} + πn

2 x = 2 π - arccos (0.25) + 2 πn

Dividir ambos os lados por

2

2 x = 2 π - arccos (0.25) + 2 πn

Dividir ambos os lados por

2

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arccos ( 0.25 )}{2} + \frac{2 πn}{2}

Simplificar

x = π - \frac{arccos ( 0.25 )}{2} + πn

x = π - \frac{arccos ( 0.25 )}{2} + πn

x = \frac{arccos ( 0.25 )}{2} + πn, x = π - \frac{arccos ( 0.25 )}{2} + πn

Mostrar soluções na forma decimal

x = \frac{1.31811 \dots}{2} + πn, x = π - \frac{1.31811 \dots}{2} + πn

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