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Popular Trigonometria >

0.84/(2pi)cos((2pi)/41.5+pi/2)

Solução

0.8 \cdot \frac{4}{2 π} cos (\frac{2 π}{4} \cdot 1.5 + \frac{π}{2})

Solução

- \frac{4 2}{5 π}

Decimal

- 0.36012 \dots

Passos da solução

0.8 \cdot \frac{4}{2 π} cos (\frac{2 π}{4} \cdot 1.5 + \frac{π}{2})

= \frac{4}{5} \cdot \frac{4}{2 π} cos (\frac{2 π}{4} \cdot \frac{3}{2} + \frac{π}{2})

Reeecreva usando identidades trigonométricas:

cos (\frac{2 π}{4} \cdot \frac{3}{2} + \frac{π}{2}) = cos (\frac{3 π}{4}) cos (\frac{π}{2}) - sin (\frac{3 π}{4}) sin (\frac{π}{2})

cos (\frac{2 π}{4} \cdot \frac{3}{2} + \frac{π}{2})

Use a identidade de soma de ângulos:

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

= cos (\frac{2 π}{4} \cdot \frac{3}{2}) cos (\frac{π}{2}) - sin (\frac{2 π}{4} \cdot \frac{3}{2}) sin (\frac{π}{2})

Simplificar:

\frac{2 π}{4} \cdot \frac{3}{2} = \frac{3 π}{4}

\frac{2 π}{4} \cdot \frac{3}{2}

Multiplicar frações:

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

= \frac{2 π 3}{4 \cdot 2}

Eliminar o fator comum:

2

= \frac{π 3}{4}

= cos (\frac{3 π}{4}) cos (\frac{π}{2}) - sin (\frac{3 π}{4}) sin (\frac{π}{2})

= \frac{4}{5} \cdot \frac{4}{2 π} (cos (\frac{3 π}{4}) cos (\frac{π}{2}) - sin (\frac{3 π}{4}) sin (\frac{π}{2}))

\frac{4}{5} \cdot \frac{4}{2 π} (cos (\frac{3 π}{4}) cos (\frac{π}{2}) - sin (\frac{3 π}{4}) sin (\frac{π}{2})) = \frac{8 ( cos ( \frac{π}{2} ) cos ( \frac{3 π}{4} ) - sin ( \frac{π}{2} ) sin ( \frac{3 π}{4} ) )}{5 π}

\frac{4}{5} \cdot \frac{4}{2 π} (cos (\frac{3 π}{4}) cos (\frac{π}{2}) - sin (\frac{3 π}{4}) sin (\frac{π}{2}))

Multiplicar frações:

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

= \frac{4 \cdot 4 ( cos ( \frac{3 π}{4} ) cos ( \frac{π}{2} ) - sin ( \frac{3 π}{4} ) sin ( \frac{π}{2} ) )}{5 \cdot 2 π}

Multiplicar os números:

4 \cdot 4 = 16

= \frac{16 ( cos ( \frac{π}{2} ) cos ( \frac{3 π}{4} ) - sin ( \frac{π}{2} ) sin ( \frac{3 π}{4} ) )}{5 \cdot 2 π}

Multiplicar os números:

5 \cdot 2 = 10

= \frac{16 ( cos ( \frac{π}{2} ) cos ( \frac{3 π}{4} ) - sin ( \frac{π}{2} ) sin ( \frac{3 π}{4} ) )}{10 π}

Eliminar o fator comum:

2

= \frac{8 ( cos ( \frac{π}{2} ) cos ( \frac{3 π}{4} ) - sin ( \frac{π}{2} ) sin ( \frac{3 π}{4} ) )}{5 π}

= \frac{8 ( cos ( \frac{π}{2} ) cos ( \frac{3 π}{4} ) - sin ( \frac{π}{2} ) sin ( \frac{3 π}{4} ) )}{5 π}

Utilizar a seguinte identidade trivial:

cos (\frac{π}{2}) = 0

cos (\frac{π}{2})

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

= 0

Utilizar a seguinte identidade trivial:

cos (\frac{3 π}{4}) = - \frac{2}{2}

cos (\frac{3 π}{4})

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

Utilizar a seguinte identidade trivial:

sin (\frac{π}{2}) = 1

sin (\frac{π}{2})

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}

= 1

Utilizar a seguinte identidade trivial:

sin (\frac{3 π}{4}) = \frac{2}{2}

sin (\frac{3 π}{4})

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}

= \frac{2}{2}

= \frac{8 ( 0 \cdot ( - \frac{2}{2} ) - 1 \cdot \frac{2}{2} )}{5 π}

Simplificar

\frac{8 ( 0 \cdot ( - \frac{2}{2} ) - 1 \cdot \frac{2}{2} )}{5 π} : - \frac{4 2}{5 π}

\frac{8 ( 0 \cdot ( - \frac{2}{2} ) - 1 \cdot \frac{2}{2} )}{5 π}

Remover os parênteses:

(- a) = - a

= \frac{8 ( - 0 \cdot \frac{2}{2} - 1 \cdot \frac{2}{2} )}{5 π}

8 (- 0 \cdot \frac{2}{2} - 1 \cdot \frac{2}{2}) = - 8 \cdot \frac{2}{2}

8 (- 0 \cdot \frac{2}{2} - 1 \cdot \frac{2}{2})

Somar elementos similares:

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

= 8 (- \frac{2}{2})

Remover os parênteses:

(- a) = - a

= - 8 \cdot \frac{2}{2}

= \frac{- 8 \cdot \frac{2}{2}}{5 π}

Aplicar as propriedades das frações:

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

= - \frac{8 \cdot \frac{2}{2}}{5 π}

Multiplicar

8 \cdot \frac{2}{2} : 42

8 \cdot \frac{2}{2}

Multiplicar frações:

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

= \frac{2 \cdot 8}{2}

Dividir:

\frac{8}{2} = 4

= 42

= - \frac{4 2}{5 π}

= - \frac{4 2}{5 π}

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0.8*4/(2pi)cos((2pi)/4*1.5+pi/2)

Solução

Solução

Exemplos populares

0.84/(2pi)cos((2pi)/41.5+pi/2)