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Popular Trigonometria >

sin(60-x)=2sin(x)

Solução

sin (6 0^{\circ} - x) = 2 sin (x)

Solução

x = 0.33347 \dots + 18 0^{\circ} n

Radianos

x = 0.33347 \dots + πn

Passos da solução

sin (6 0^{\circ} - x) = 2 sin (x)

Reeecreva usando identidades trigonométricas

sin (6 0^{\circ} - x) = 2 sin (x)

Reeecreva usando identidades trigonométricas

sin (6 0^{\circ} - x)

Use a identidade de diferença de ângulos:

sin (s - t) = sin (s) cos (t) - cos (s) sin (t)

= sin (6 0^{\circ}) cos (x) - cos (6 0^{\circ}) sin (x)

Simplificar

sin (6 0^{\circ}) cos (x) - cos (6 0^{\circ}) sin (x) : \frac{3}{2} cos (x) - \frac{1}{2} sin (x)

sin (6 0^{\circ}) cos (x) - cos (6 0^{\circ}) sin (x)

Simplificar

sin (6 0^{\circ}) : \frac{3}{2}

sin (6 0^{\circ})

Utilizar a seguinte identidade trivial:

sin (6 0^{\circ}) = \frac{3}{2}

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}{2}

= \frac{3}{2} cos (x) - cos (6 0^{\circ}) sin (x)

Simplificar

cos (6 0^{\circ}) : \frac{1}{2}

cos (6 0^{\circ})

Utilizar a seguinte identidade trivial:

cos (6 0^{\circ}) = \frac{1}{2}

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{1}{2}

= \frac{3}{2} cos (x) - \frac{1}{2} sin (x)

= \frac{3}{2} cos (x) - \frac{1}{2} sin (x)

\frac{3}{2} cos (x) - \frac{1}{2} sin (x) = 2 sin (x)

\frac{3}{2} cos (x) - \frac{1}{2} sin (x) = 2 sin (x)

Subtrair

2 sin (x)

de ambos os lados

\frac{3}{2} cos (x) - \frac{5}{2} sin (x) = 0

Simplificar

\frac{3}{2} cos (x) - \frac{5}{2} sin (x) : \frac{3 cos ( x ) - 5 sin ( x )}{2}

\frac{3}{2} cos (x) - \frac{5}{2} sin (x)

Multiplicar

\frac{3}{2} cos (x) : \frac{3 cos ( x )}{2}

\frac{3}{2} cos (x)

Multiplicar frações:

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

= \frac{3 cos ( x )}{2}

= \frac{3 cos ( x )}{2} - \frac{5}{2} sin (x)

Multiplicar

\frac{5}{2} sin (x) : \frac{5 sin ( x )}{2}

\frac{5}{2} sin (x)

Multiplicar frações:

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

= \frac{5 sin ( x )}{2}

= \frac{3 cos ( x )}{2} - \frac{5 sin ( x )}{2}

Aplicar a regra

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

= \frac{3 cos ( x ) - 5 sin ( x )}{2}

\frac{3 cos ( x ) - 5 sin ( x )}{2} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

3 cos (x) - 5 sin (x) = 0

Reeecreva usando identidades trigonométricas

3 cos (x) - 5 sin (x) = 0

Dividir ambos os lados por

cos (x), cos (x) \neq = 0

\frac{3 cos ( x ) - 5 sin ( x )}{cos ( x )} = \frac{0}{cos ( x )}

Simplificar

3 - \frac{5 sin ( x )}{cos ( x )} = 0

Utilizar a Identidade Básica da Trigonometria:

\frac{sin ( x )}{cos ( x )} = tan (x)

3 - 5 tan (x) = 0

3 - 5 tan (x) = 0

Mova

3

para o lado direito

3 - 5 tan (x) = 0

Subtrair

3

de ambos os lados

3 - 5 tan (x) - 3 = 0 - 3

Simplificar

- 5 tan (x) = - 3

- 5 tan (x) = - 3

Dividir ambos os lados por

- 5

- 5 tan (x) = - 3

Dividir ambos os lados por

- 5

\frac{- 5 tan ( x )}{- 5} = \frac{- 3}{- 5}

Simplificar

tan (x) = \frac{3}{5}

tan (x) = \frac{3}{5}

Aplique as propriedades trigonométricas inversas

tan (x) = \frac{3}{5}

Soluções gerais para

tan (x) = \frac{3}{5}

tan (x) = a \Rightarrow x = arctan (a) + 18 0^{\circ} n

x = arctan (\frac{3}{5}) + 18 0^{\circ} n

x = arctan (\frac{3}{5}) + 18 0^{\circ} n

Mostrar soluções na forma decimal

x = 0.33347 \dots + 18 0^{\circ} n

Gráfico

Exemplos populares

tan(x)=pi

tan (x) = π

sinh(x)= 5/12

sinh (x) = \frac{5}{12}

1-2sin^2(x/2)=2cos^2(x)

1 - 2 sin^{2} (\frac{x}{2}) = 2 cos^{2} (x)

10sin(x)+1=3-2sin(x)

10 sin (x) + 1 = 3 - 2 sin (x)

2cos(x)-9=-4sec(x)

2 cos (x) - 9 = - 4 sec (x)