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Popular >

3sin(2y)-4sin(2y)cos(2y)=0

Solução

3 sin (2 y) - 4 sin (2 y) cos (2 y) = 0

Solução

y = πn, y = \frac{π}{2} + πn, y = \frac{0.72273 \dots}{2} + πn, y = π - \frac{0.72273 \dots}{2} + πn

Graus

y = 0^{\circ} + 18 0^{\circ} n, y = 9 0^{\circ} + 18 0^{\circ} n, y = 20.70481 \dots^{\circ} + 18 0^{\circ} n, y = 159.29518 \dots^{\circ} + 18 0^{\circ} n

Passos da solução

3 sin (2 y) - 4 sin (2 y) cos (2 y) = 0

Fatorar

3 sin (2 y) - 4 sin (2 y) cos (2 y) : - sin (2 y) (4 cos (2 y) - 3)

3 sin (2 y) - 4 sin (2 y) cos (2 y)

Fatorar o termo comum

- sin (2 y)

= - sin (2 y) (- 3 + 4 cos (2 y))

- sin (2 y) (4 cos (2 y) - 3) = 0

Resolver cada parte separadamente

sin (2 y) = 0 or 4 cos (2 y) - 3 = 0

sin (2 y) = 0 : y = πn, y = \frac{π}{2} + πn

sin (2 y) = 0

Soluções gerais para

sin (2 y) = 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}

2 y = 0 + 2 πn, 2 y = π + 2 πn

2 y = 0 + 2 πn, 2 y = π + 2 πn

Resolver

2 y = 0 + 2 πn : y = πn

2 y = 0 + 2 πn

0 + 2 πn = 2 πn

2 y = 2 πn

Dividir ambos os lados por

2

2 y = 2 πn

Dividir ambos os lados por

2

\frac{2 y}{2} = \frac{2 πn}{2}

Simplificar

y = πn

y = πn

Resolver

2 y = π + 2 πn : y = \frac{π}{2} + πn

2 y = π + 2 πn

Dividir ambos os lados por

2

2 y = π + 2 πn

Dividir ambos os lados por

2

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

Simplificar

y = \frac{π}{2} + πn

y = \frac{π}{2} + πn

y = πn, y = \frac{π}{2} + πn

4 cos (2 y) - 3 = 0 : y = \frac{arccos ( \frac{3}{4} )}{2} + πn, y = π - \frac{arccos ( \frac{3}{4} )}{2} + πn

4 cos (2 y) - 3 = 0

Mova

3

para o lado direito

4 cos (2 y) - 3 = 0

Adicionar

3

a ambos os lados

4 cos (2 y) - 3 + 3 = 0 + 3

Simplificar

4 cos (2 y) = 3

4 cos (2 y) = 3

Dividir ambos os lados por

4

4 cos (2 y) = 3

Dividir ambos os lados por

4

\frac{4 cos ( 2 y )}{4} = \frac{3}{4}

Simplificar

cos (2 y) = \frac{3}{4}

cos (2 y) = \frac{3}{4}

Aplique as propriedades trigonométricas inversas

cos (2 y) = \frac{3}{4}

Soluções gerais para

cos (2 y) = \frac{3}{4}

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

2 y = arccos (\frac{3}{4}) + 2 πn, 2 y = 2 π - arccos (\frac{3}{4}) + 2 πn

2 y = arccos (\frac{3}{4}) + 2 πn, 2 y = 2 π - arccos (\frac{3}{4}) + 2 πn

Resolver

2 y = arccos (\frac{3}{4}) + 2 πn : y = \frac{arccos ( \frac{3}{4} )}{2} + πn

2 y = arccos (\frac{3}{4}) + 2 πn

Dividir ambos os lados por

2

2 y = arccos (\frac{3}{4}) + 2 πn

Dividir ambos os lados por

2

\frac{2 y}{2} = \frac{arccos ( \frac{3}{4} )}{2} + \frac{2 πn}{2}

Simplificar

y = \frac{arccos ( \frac{3}{4} )}{2} + πn

y = \frac{arccos ( \frac{3}{4} )}{2} + πn

Resolver

2 y = 2 π - arccos (\frac{3}{4}) + 2 πn : y = π - \frac{arccos ( \frac{3}{4} )}{2} + πn

2 y = 2 π - arccos (\frac{3}{4}) + 2 πn

Dividir ambos os lados por

2

2 y = 2 π - arccos (\frac{3}{4}) + 2 πn

Dividir ambos os lados por

2

\frac{2 y}{2} = \frac{2 π}{2} - \frac{arccos ( \frac{3}{4} )}{2} + \frac{2 πn}{2}

Simplificar

y = π - \frac{arccos ( \frac{3}{4} )}{2} + πn

y = π - \frac{arccos ( \frac{3}{4} )}{2} + πn

y = \frac{arccos ( \frac{3}{4} )}{2} + πn, y = π - \frac{arccos ( \frac{3}{4} )}{2} + πn

Combinar toda as soluções

y = πn, y = \frac{π}{2} + πn, y = \frac{arccos ( \frac{3}{4} )}{2} + πn, y = π - \frac{arccos ( \frac{3}{4} )}{2} + πn

Mostrar soluções na forma decimal

y = πn, y = \frac{π}{2} + πn, y = \frac{0.72273 \dots}{2} + πn, y = π - \frac{0.72273 \dots}{2} + πn

Exemplos populares

sin(x)+sin(4x)=0

sin (x) + sin (4 x) = 0

cos(0.568x-2.595)=0

cos (0.568 x - 2.595) = 0

8tan(-x+pi/8)=8

8 tan (- x + \frac{π}{8}) = 8

tan(A/2)=sqrt(0.62)

tan (\frac{A}{2}) = 0.62

2sin(θ)-1=0,(0,2pi)

2 sin (θ) - 1 = 0, (0, 2 π)