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Popular Trigonometria >

(sin(55.01-x))/(sin(x))= 1200/500

Solução

\frac{sin ( 55.01 - x )}{sin ( x )} = \frac{1200}{500}

Solução

x = 2.75168 \dots + πn

Graus

x = 157.65972 \dots^{\circ} + 18 0^{\circ} n

Passos da solução

\frac{sin ( 55.01 - x )}{sin ( x )} = \frac{1200}{500}

Reeecreva usando identidades trigonométricas

\frac{sin ( 55.01 - x )}{sin ( x )} = \frac{1200}{500}

Reeecreva usando identidades trigonométricas

sin (55.01 - x)

Use a identidade de diferença de ângulos:

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

= sin (55.01) cos (x) - cos (55.01) sin (x)

Simplificar

sin (55.01) cos (x) - cos (55.01) sin (x) : - 0.99948 \dots cos (x) - 0.03212 \dots sin (x)

sin (55.01) cos (x) - cos (55.01) sin (x)

Simplificar

sin (55.01) : - 0.99948 \dots

sin (55.01)

sin (55.01) = - 0.99948 \dots

= - 0.99948 \dots

= - 0.99948 \dots cos (x) - cos (55.01) sin (x)

Simplificar

cos (55.01) : 0.03212 \dots

cos (55.01)

cos (55.01) = 0.03212 \dots

= 0.03212 \dots

= - 0.99948 \dots cos (x) - 0.03212 \dots sin (x)

= - 0.99948 \dots cos (x) - 0.03212 \dots sin (x)

\frac{- 0.99948 \dots cos ( x ) - 0.03212 \dots sin ( x )}{sin ( x )} = \frac{1200}{500}

\frac{1200}{500} = \frac{12}{5}

\frac{1200}{500}

Eliminar o fator comum:

100

= \frac{12}{5}

\frac{- 0.99948 \dots cos ( x ) - 0.03212 \dots sin ( x )}{sin ( x )} = \frac{12}{5}

\frac{- 0.99948 \dots cos ( x ) - 0.03212 \dots sin ( x )}{sin ( x )} = \frac{12}{5}

Subtrair

\frac{12}{5}

de ambos os lados

\frac{- 0.99948 \dots cos ( x ) - 0.03212 \dots sin ( x )}{sin ( x )} - 2.4 = 0

Reeecreva usando identidades trigonométricas

- 2.4 + \frac{- 0.03212 \dots sin ( x ) - 0.99948 \dots cos ( x )}{sin ( x )}

Utilizar a Identidade Básica da Trigonometria:

sin (x) = \frac{1}{csc ( x )}

= - 2.4 + \frac{- 0.03212 \dots \cdot \frac{1}{c s c ( x )} - 0.99948 \dots cos ( x )}{\frac{1}{c s c ( x )}}

Simplificar

- 2.4 + \frac{- 0.03212 \dots \cdot \frac{1}{c s c ( x )} - 0.99948 \dots cos ( x )}{\frac{1}{c s c ( x )}} : - 0.99948 \dots csc (x) cos (x) - 2.43212 \dots

- 2.4 + \frac{- 0.03212 \dots \cdot \frac{1}{c s c ( x )} - 0.99948 \dots cos ( x )}{\frac{1}{c s c ( x )}}

\frac{- 0.03212 \dots \cdot \frac{1}{c s c ( x )} - 0.99948 \dots cos ( x )}{\frac{1}{c s c ( x )}} = csc (x) (- \frac{0.03212 \dots}{csc ( x )} - 0.99948 \dots cos (x))

\frac{- 0.03212 \dots \cdot \frac{1}{c s c ( x )} - 0.99948 \dots cos ( x )}{\frac{1}{c s c ( x )}}

Aplicar as propriedades das frações:

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

= \frac{( - 0.03212 \dots \cdot \frac{1}{c s c ( x )} - 0.99948 \dots cos ( x ) ) csc ( x )}{1}

0.03212 \dots \cdot \frac{1}{csc ( x )} = \frac{0.03212 \dots}{csc ( x )}

0.03212 \dots \cdot \frac{1}{csc ( x )}

Multiplicar frações:

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

= \frac{1 \cdot 0.03212 \dots}{csc ( x )}

Multiplicar os números:

1 \cdot 0.03212 \dots = 0.03212 \dots

= \frac{0.03212 \dots}{csc ( x )}

= \frac{csc ( x ) ( - \frac{0.03212 \dots}{c s c ( x )} - 0.99948 \dots cos ( x ) )}{1}

Aplicar as propriedades das frações:

\frac{a}{1} = a

= (- \frac{0.03212 \dots}{csc ( x )} - 0.99948 \dots cos (x)) csc (x)

= - 2.4 + csc (x) (- \frac{0.03212 \dots}{csc ( x )} - 0.99948 \dots cos (x))

= - 2.4 + csc (x) (- \frac{0.03212 \dots}{csc ( x )} - 0.99948 \dots cos (x))

Expandir

csc (x) (- \frac{0.03212 \dots}{csc ( x )} - 0.99948 \dots cos (x)) : - 0.03212 \dots - 0.99948 \dots csc (x) cos (x)

csc (x) (- \frac{0.03212 \dots}{csc ( x )} - 0.99948 \dots cos (x))

Colocar os parênteses utilizando:

a (b - c) = ab - a c

a = csc (x), b = - \frac{0.03212 \dots}{csc ( x )}, c = 0.99948 \dots cos (x)

= csc (x) (- \frac{0.03212 \dots}{csc ( x )}) - csc (x) \cdot 0.99948 \dots cos (x)

Aplicar as regras dos sinais

+ (- a) = - a

= - \frac{0.03212 \dots}{csc ( x )} csc (x) - 0.99948 \dots csc (x) cos (x)

\frac{0.03212 \dots}{csc ( x )} csc (x) = 0.03212 \dots

\frac{0.03212 \dots}{csc ( x )} csc (x)

Multiplicar frações:

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

= \frac{0.03212 \dots csc ( x )}{csc ( x )}

Eliminar o fator comum:

csc (x)

= 0.03212 \dots

= - 0.03212 \dots - 0.99948 \dots csc (x) cos (x)

= - 2.4 - 0.03212 \dots - 0.99948 \dots csc (x) cos (x)

Subtrair:

- 2.4 - 0.03212 \dots = - 2.43212 \dots

= - 0.99948 \dots csc (x) cos (x) - 2.43212 \dots

= - 0.99948 \dots csc (x) cos (x) - 2.43212 \dots

csc (x) cos (x) = cot (x)

csc (x) cos (x)

Expresar com seno, cosseno

csc (x) cos (x)

Utilizar a Identidade Básica da Trigonometria:

csc (x) = \frac{1}{sin ( x )}

= \frac{1}{sin ( x )} cos (x)

Simplificar

\frac{1}{sin ( x )} cos (x) : \frac{cos ( x )}{sin ( x )}

\frac{1}{sin ( x )} cos (x)

Multiplicar frações:

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

= \frac{1 cos ( x )}{sin ( x )}

Multiplicar:

1 \cdot cos (x) = cos (x)

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

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

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

Utilizar a Identidade Básica da Trigonometria:

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

= cot (x)

= - 2.43212 \dots - 0.99948 \dots cot (x)

- 2.43212 \dots - 0.99948 \dots cot (x) = 0

Mova

2.43212 \dots

para o lado direito

- 2.43212 \dots - 0.99948 \dots cot (x) = 0

Adicionar

2.43212 \dots

a ambos os lados

- 2.43212 \dots - 0.99948 \dots cot (x) + 2.43212 \dots = 0 + 2.43212 \dots

Simplificar

- 0.99948 \dots cot (x) = 2.43212 \dots

- 0.99948 \dots cot (x) = 2.43212 \dots

Dividir ambos os lados por

- 0.99948 \dots

- 0.99948 \dots cot (x) = 2.43212 \dots

Dividir ambos os lados por

- 0.99948 \dots

\frac{- 0.99948 \dots cot ( x )}{- 0.99948 \dots} = \frac{2.43212 \dots}{- 0.99948 \dots}

Simplificar

\frac{- 0.99948 \dots cot ( x )}{- 0.99948 \dots} = \frac{2.43212 \dots}{- 0.99948 \dots}

Simplificar

\frac{- 0.99948 \dots cot ( x )}{- 0.99948 \dots} : cot (x)

\frac{- 0.99948 \dots cot ( x )}{- 0.99948 \dots}

Aplicar as propriedades das frações:

\frac{- a}{- b} = \frac{a}{b}

= \frac{0.99948 \dots cot ( x )}{0.99948 \dots}

Eliminar o fator comum:

0.99948 \dots

= cot (x)

Simplificar

\frac{2.43212 \dots}{- 0.99948 \dots} : - 2.43337 \dots

\frac{2.43212 \dots}{- 0.99948 \dots}

Aplicar as propriedades das frações:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{2.43212 \dots}{0.99948 \dots}

Dividir:

\frac{2.43212 \dots}{0.99948 \dots} = 2.43337 \dots

= - 2.43337 \dots

cot (x) = - 2.43337 \dots

cot (x) = - 2.43337 \dots

cot (x) = - 2.43337 \dots

Aplique as propriedades trigonométricas inversas

cot (x) = - 2.43337 \dots

Soluções gerais para

cot (x) = - 2.43337 \dots

cot (x) = - a \Rightarrow x = arccot (- a) + πn

x = arccot (- 2.43337 \dots) + πn

x = arccot (- 2.43337 \dots) + πn

Mostrar soluções na forma decimal

x = 2.75168 \dots + πn

Gráfico

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