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Popular Trigonometria >

sin((3x)/2+45)=0

Solução

sin (\frac{3 x}{2} + 4 5^{\circ}) = 0

Solução

x = \frac{72 0 ^{\circ} n}{3} - 3 0^{\circ}, x = - 3 0^{\circ} + 12 0^{\circ} + \frac{72 0 ^{\circ} n}{3}

Radianos

x = - \frac{π}{6} + \frac{4 π}{3} n, x = - \frac{π}{6} + \frac{2 π}{3} + \frac{4 π}{3} n

Passos da solução

sin (\frac{3 x}{2} + 4 5^{\circ}) = 0

Soluções gerais para

sin (\frac{3 x}{2} + 4 5^{\circ}) = 0

sin (x)

tabela de periodicidade com ciclo de

36 0^{\circ} n

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

\frac{3 x}{2} + 4 5^{\circ} = 0 + 36 0^{\circ} n, \frac{3 x}{2} + 4 5^{\circ} = 18 0^{\circ} + 36 0^{\circ} n

\frac{3 x}{2} + 4 5^{\circ} = 0 + 36 0^{\circ} n, \frac{3 x}{2} + 4 5^{\circ} = 18 0^{\circ} + 36 0^{\circ} n

Resolver

\frac{3 x}{2} + 4 5^{\circ} = 0 + 36 0^{\circ} n : x = \frac{72 0 ^{\circ} n}{3} - 3 0^{\circ}

\frac{3 x}{2} + 4 5^{\circ} = 0 + 36 0^{\circ} n

0 + 36 0^{\circ} n = 36 0^{\circ} n

\frac{3 x}{2} + 4 5^{\circ} = 36 0^{\circ} n

Mova

4 5^{\circ}

para o lado direito

\frac{3 x}{2} + 4 5^{\circ} = 36 0^{\circ} n

Subtrair

4 5^{\circ}

de ambos os lados

\frac{3 x}{2} + 4 5^{\circ} - 4 5^{\circ} = 36 0^{\circ} n - 4 5^{\circ}

Simplificar

\frac{3 x}{2} = 36 0^{\circ} n - 4 5^{\circ}

\frac{3 x}{2} = 36 0^{\circ} n - 4 5^{\circ}

Multiplicar ambos os lados por

2

\frac{3 x}{2} = 36 0^{\circ} n - 4 5^{\circ}

Multiplicar ambos os lados por

2

\frac{2 \cdot 3 x}{2} = 2 \cdot 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

Simplificar

\frac{2 \cdot 3 x}{2} = 2 \cdot 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

Simplificar

\frac{2 \cdot 3 x}{2} : 3 x

\frac{2 \cdot 3 x}{2}

Multiplicar os números:

2 \cdot 3 = 6

= \frac{6 x}{2}

Dividir:

\frac{6}{2} = 3

= 3 x

Simplificar

2 \cdot 36 0^{\circ} n - 2 \cdot 4 5^{\circ} : 72 0^{\circ} n - 9 0^{\circ}

2 \cdot 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

2 \cdot 36 0^{\circ} n = 72 0^{\circ} n

2 \cdot 36 0^{\circ} n

Multiplicar os números:

2 \cdot 2 = 4

= 72 0^{\circ} n

2 \cdot 4 5^{\circ} = 9 0^{\circ}

2 \cdot 4 5^{\circ}

Multiplicar frações:

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

= 9 0^{\circ}

Eliminar o fator comum:

2

= 9 0^{\circ}

= 72 0^{\circ} n - 9 0^{\circ}

3 x = 72 0^{\circ} n - 9 0^{\circ}

3 x = 72 0^{\circ} n - 9 0^{\circ}

3 x = 72 0^{\circ} n - 9 0^{\circ}

Dividir ambos os lados por

3

3 x = 72 0^{\circ} n - 9 0^{\circ}

Dividir ambos os lados por

3

\frac{3 x}{3} = \frac{72 0 ^{\circ} n}{3} - \frac{9 0 ^{\circ}}{3}

Simplificar

\frac{3 x}{3} = \frac{72 0 ^{\circ} n}{3} - \frac{9 0 ^{\circ}}{3}

Simplificar

\frac{3 x}{3} : x

\frac{3 x}{3}

Dividir:

\frac{3}{3} = 1

= x

Simplificar

\frac{72 0 ^{\circ} n}{3} - \frac{9 0 ^{\circ}}{3} : \frac{72 0 ^{\circ} n}{3} - 3 0^{\circ}

\frac{72 0 ^{\circ} n}{3} - \frac{9 0 ^{\circ}}{3}

\frac{9 0 ^{\circ}}{3} = 3 0^{\circ}

\frac{9 0 ^{\circ}}{3}

Aplicar as propriedades das frações:

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

= \frac{18 0 ^{\circ}}{2 \cdot 3}

Multiplicar os números:

2 \cdot 3 = 6

= 3 0^{\circ}

= \frac{72 0 ^{\circ} n}{3} - 3 0^{\circ}

x = \frac{72 0 ^{\circ} n}{3} - 3 0^{\circ}

x = \frac{72 0 ^{\circ} n}{3} - 3 0^{\circ}

x = \frac{72 0 ^{\circ} n}{3} - 3 0^{\circ}

Resolver

\frac{3 x}{2} + 4 5^{\circ} = 18 0^{\circ} + 36 0^{\circ} n : x = - 3 0^{\circ} + 12 0^{\circ} + \frac{72 0 ^{\circ} n}{3}

\frac{3 x}{2} + 4 5^{\circ} = 18 0^{\circ} + 36 0^{\circ} n

Mova

4 5^{\circ}

para o lado direito

\frac{3 x}{2} + 4 5^{\circ} = 18 0^{\circ} + 36 0^{\circ} n

Subtrair

4 5^{\circ}

de ambos os lados

\frac{3 x}{2} + 4 5^{\circ} - 4 5^{\circ} = 18 0^{\circ} + 36 0^{\circ} n - 4 5^{\circ}

Simplificar

\frac{3 x}{2} = 18 0^{\circ} + 36 0^{\circ} n - 4 5^{\circ}

\frac{3 x}{2} = 18 0^{\circ} + 36 0^{\circ} n - 4 5^{\circ}

Multiplicar ambos os lados por

2

\frac{3 x}{2} = 18 0^{\circ} + 36 0^{\circ} n - 4 5^{\circ}

Multiplicar ambos os lados por

2

\frac{2 \cdot 3 x}{2} = 36 0^{\circ} + 2 \cdot 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

Simplificar

\frac{2 \cdot 3 x}{2} = 36 0^{\circ} + 2 \cdot 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

Simplificar

\frac{2 \cdot 3 x}{2} : 3 x

\frac{2 \cdot 3 x}{2}

Multiplicar os números:

2 \cdot 3 = 6

= \frac{6 x}{2}

Dividir:

\frac{6}{2} = 3

= 3 x

Simplificar

36 0^{\circ} + 2 \cdot 36 0^{\circ} n - 2 \cdot 4 5^{\circ} : 36 0^{\circ} + 72 0^{\circ} n - 9 0^{\circ}

36 0^{\circ} + 2 \cdot 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

2 \cdot 36 0^{\circ} n = 72 0^{\circ} n

2 \cdot 36 0^{\circ} n

Multiplicar os números:

2 \cdot 2 = 4

= 72 0^{\circ} n

2 \cdot 4 5^{\circ} = 9 0^{\circ}

2 \cdot 4 5^{\circ}

Multiplicar frações:

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

= 9 0^{\circ}

Eliminar o fator comum:

2

= 9 0^{\circ}

= 36 0^{\circ} + 72 0^{\circ} n - 9 0^{\circ}

3 x = 36 0^{\circ} + 72 0^{\circ} n - 9 0^{\circ}

3 x = 36 0^{\circ} + 72 0^{\circ} n - 9 0^{\circ}

3 x = 36 0^{\circ} + 72 0^{\circ} n - 9 0^{\circ}

Dividir ambos os lados por

3

3 x = 36 0^{\circ} + 72 0^{\circ} n - 9 0^{\circ}

Dividir ambos os lados por

3

\frac{3 x}{3} = 12 0^{\circ} + \frac{72 0 ^{\circ} n}{3} - \frac{9 0 ^{\circ}}{3}

Simplificar

\frac{3 x}{3} = 12 0^{\circ} + \frac{72 0 ^{\circ} n}{3} - \frac{9 0 ^{\circ}}{3}

Simplificar

\frac{3 x}{3} : x

\frac{3 x}{3}

Dividir:

\frac{3}{3} = 1

= x

Simplificar

12 0^{\circ} + \frac{72 0 ^{\circ} n}{3} - \frac{9 0 ^{\circ}}{3} : - 3 0^{\circ} + 12 0^{\circ} + \frac{72 0 ^{\circ} n}{3}

12 0^{\circ} + \frac{72 0 ^{\circ} n}{3} - \frac{9 0 ^{\circ}}{3}

\frac{9 0 ^{\circ}}{3} = 3 0^{\circ}

\frac{9 0 ^{\circ}}{3}

Aplicar as propriedades das frações:

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

= \frac{18 0 ^{\circ}}{2 \cdot 3}

Multiplicar os números:

2 \cdot 3 = 6

= 3 0^{\circ}

= 12 0^{\circ} + \frac{72 0 ^{\circ} n}{3} - 3 0^{\circ}

Agrupar termos semelhantes

= - 3 0^{\circ} + 12 0^{\circ} + \frac{72 0 ^{\circ} n}{3}

x = - 3 0^{\circ} + 12 0^{\circ} + \frac{72 0 ^{\circ} n}{3}

x = - 3 0^{\circ} + 12 0^{\circ} + \frac{72 0 ^{\circ} n}{3}

x = - 3 0^{\circ} + 12 0^{\circ} + \frac{72 0 ^{\circ} n}{3}

x = \frac{72 0 ^{\circ} n}{3} - 3 0^{\circ}, x = - 3 0^{\circ} + 12 0^{\circ} + \frac{72 0 ^{\circ} n}{3}

Gráfico

Exemplos populares

4sin(2θ)-5sin(θ)=0

4 sin (2 θ) - 5 sin (θ) = 0

sin^2(x)-cos^2(x)=sin(x)

sin^{2} (x) - cos^{2} (x) = sin (x)

4cos(2θ)+11sin(θ)-4=3

4 cos (2 θ) + 11 sin (θ) - 4 = 3

cos(x)= 5/15

cos (x) = \frac{5}{15}

(cot(θ)+1)(csc(θ)-1/2)=0

(cot (θ) + 1) (csc (θ) - \frac{1}{2}) = 0