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Popular Trigonometria >

(sin(120)cos(210)tan(315)cos(27))/(sin(63)cos(540))

Solução

\frac{sin ( 12 0 ^{\circ} ) cos ( 21 0 ^{\circ} ) tan ( 31 5 ^{\circ} ) cos ( 2 7 ^{\circ} )}{sin ( 6 3 ^{\circ} ) cos ( 54 0 ^{\circ} )}

Solução

- \frac{3}{4}

Decimal

- 0.75

Passos da solução

\frac{sin ( 12 0 ^{\circ} ) cos ( 21 0 ^{\circ} ) tan ( 31 5 ^{\circ} ) cos ( 2 7 ^{\circ} )}{sin ( 6 3 ^{\circ} ) cos ( 54 0 ^{\circ} )}

tan (31 5^{\circ}) = tan (13 5^{\circ})

tan (31 5^{\circ})

Reescrever

31 5^{\circ}

como

18 0^{\circ} + 13 5^{\circ}

= tan (18 0^{\circ} + 13 5^{\circ})

Utilizar a periodicidade de

tan

tan (x + 18 0^{\circ}) = tan (x)

tan (18 0^{\circ} + 13 5^{\circ}) = tan (13 5^{\circ})

= tan (13 5^{\circ})

= \frac{sin ( 12 0 ^{\circ} ) cos ( 21 0 ^{\circ} ) tan ( 13 5 ^{\circ} ) cos ( 2 7 ^{\circ} )}{sin ( 6 3 ^{\circ} ) cos ( 54 0 ^{\circ} )}

cos (54 0^{\circ}) = cos (18 0^{\circ})

cos (54 0^{\circ})

Reescrever

54 0^{\circ}

como

36 0^{\circ} + 18 0^{\circ}

= cos (36 0^{\circ} + 18 0^{\circ})

Utilizar a periodicidade de

cos

cos (x + 36 0^{\circ}) = cos (x)

cos (36 0^{\circ} + 18 0^{\circ}) = cos (18 0^{\circ})

= cos (18 0^{\circ})

= \frac{sin ( 12 0 ^{\circ} ) cos ( 21 0 ^{\circ} ) tan ( 13 5 ^{\circ} ) cos ( 2 7 ^{\circ} )}{sin ( 6 3 ^{\circ} ) cos ( 18 0 ^{\circ} )}

Reeecreva usando identidades trigonométricas:

sin (6 3^{\circ}) = cos (2 7^{\circ})

sin (6 3^{\circ})

Usar a seguinte identidade:

sin (x) = cos (9 0^{\circ} - x)

= cos (9 0^{\circ} - 6 3^{\circ})

Simplificar

= cos (2 7^{\circ})

= \frac{sin ( 12 0 ^{\circ} ) cos ( 21 0 ^{\circ} ) tan ( 13 5 ^{\circ} ) cos ( 2 7 ^{\circ} )}{cos ( 2 7 ^{\circ} ) cos ( 18 0 ^{\circ} )}

Simplificar

= \frac{sin ( 12 0 ^{\circ} ) cos ( 21 0 ^{\circ} ) tan ( 13 5 ^{\circ} )}{cos ( 18 0 ^{\circ} )}

Utilizar a seguinte identidade trivial:

sin (12 0^{\circ}) = \frac{3}{2}

sin (12 0^{\circ})

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}

Reeecreva usando identidades trigonométricas:

cos (21 0^{\circ}) = - \frac{3}{2}

cos (21 0^{\circ})

Reeecreva usando identidades trigonométricas:

cos (18 0^{\circ}) cos (3 0^{\circ}) - sin (18 0^{\circ}) sin (3 0^{\circ})

cos (21 0^{\circ})

Escrever

cos (21 0^{\circ})

como

cos (18 0^{\circ} + 3 0^{\circ})

= cos (18 0^{\circ} + 3 0^{\circ})

Use a identidade de soma de ângulos:

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

= cos (18 0^{\circ}) cos (3 0^{\circ}) - sin (18 0^{\circ}) sin (3 0^{\circ})

= cos (18 0^{\circ}) cos (3 0^{\circ}) - sin (18 0^{\circ}) sin (3 0^{\circ})

Utilizar a seguinte identidade trivial:

cos (18 0^{\circ}) = (- 1)

cos (18 0^{\circ})

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}

= (- 1)

Utilizar a seguinte identidade trivial:

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

cos (3 0^{\circ})

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{3}{2}

Utilizar a seguinte identidade trivial:

sin (18 0^{\circ}) = 0

sin (18 0^{\circ})

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}

= 0

Utilizar a seguinte identidade trivial:

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 0^{\circ})

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{1}{2}

= (- 1) \frac{3}{2} - 0 \cdot \frac{1}{2}

Simplificar

= - \frac{3}{2}

Reeecreva usando identidades trigonométricas:

tan (13 5^{\circ}) = - 1

tan (13 5^{\circ})

Reeecreva usando identidades trigonométricas:

\frac{sin ( 13 5 ^{\circ} )}{cos ( 13 5 ^{\circ} )}

tan (13 5^{\circ})

Utilizar a Identidade Básica da Trigonometria:

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

= \frac{sin ( 13 5 ^{\circ} )}{cos ( 13 5 ^{\circ} )}

= \frac{sin ( 13 5 ^{\circ} )}{cos ( 13 5 ^{\circ} )}

Utilizar a seguinte identidade trivial:

sin (13 5^{\circ}) = \frac{2}{2}

sin (13 5^{\circ})

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{2}{2}

Utilizar a seguinte identidade trivial:

cos (13 5^{\circ}) = - \frac{2}{2}

cos (13 5^{\circ})

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{2}{2}

= \frac{\frac{2}{2}}{- \frac{2}{2}}

Simplificar

\frac{\frac{2}{2}}{- \frac{2}{2}} : - 1

\frac{\frac{2}{2}}{- \frac{2}{2}}

Aplicar as propriedades das frações:

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

= - \frac{\frac{2}{2}}{\frac{2}{2}}

Dividir frações:

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

= - \frac{2 \cdot 2}{2 2}

Eliminar o fator comum:

2

= - \frac{2}{2}

Eliminar o fator comum:

2

= - 1

= - 1

Utilizar a seguinte identidade trivial:

cos (18 0^{\circ}) = (- 1)

cos (18 0^{\circ})

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}

= (- 1)

= \frac{\frac{3}{2} ( - \frac{3}{2} ) ( - 1 )}{- 1}

Simplificar

\frac{\frac{3}{2} ( - \frac{3}{2} ) ( - 1 )}{- 1} : - \frac{3}{4}

\frac{\frac{3}{2} ( - \frac{3}{2} ) ( - 1 )}{- 1}

Remover os parênteses:

(- a) = - a, - (- a) = a

= \frac{\frac{3}{2} \cdot \frac{3}{2} \cdot 1}{- 1}

Multiplicar:

\frac{3}{2} \cdot 1 = \frac{3}{2}

= \frac{\frac{3}{2} \cdot \frac{3}{2}}{- 1}

Aplicar as propriedades das frações:

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

= - \frac{\frac{3}{2} \cdot \frac{3}{2}}{1}

Aplicar as propriedades das frações:

\frac{a}{1} = a

\frac{\frac{3}{2} \cdot \frac{3}{2}}{1} = \frac{3}{2} \cdot \frac{3}{2}

= - \frac{3}{2} \cdot \frac{3}{2}

Multiplicar frações:

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

= - \frac{3 3}{2 \cdot 2}

33 = 3

33

Aplicar as propriedades dos radicais:

a a = a

33 = 3

= 3

= - \frac{3}{2 \cdot 2}

Multiplicar os números:

2 \cdot 2 = 4

= - \frac{3}{4}

= - \frac{3}{4}

Exemplos populares

6*sin(35)

6 \cdot sin (3 5^{\circ})

8*sin(65)

8 \cdot sin (6 5^{\circ})

csc((2pi)/5)

csc (\frac{2 π}{5})

cos(pi/2*4)

cos (\frac{π}{2} \cdot 4)

(15)/(tan(70))

\frac{15}{tan ( 7 0 ^{\circ} )}