English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Trigonometria >

11=12+3.5sin((2pi)/(365)t)

Solução

11 = 12 + 3.5 sin (\frac{2 π}{365} t)

Solução

t = - \frac{365 \cdot 0.28975 \dots}{2 π} + 365 n, t = \frac{365}{2} + \frac{365 \cdot 0.28975 \dots}{2 π} + 365 n

Graus

t = - 964.40981 \dots^{\circ} + 20912.95952 \dots^{\circ} n, t = 11420.88957 \dots^{\circ} + 20912.95952 \dots^{\circ} n

Passos da solução

11 = 12 + 3.5 sin (\frac{2 π}{365} t)

Trocar lados

12 + 3.5 sin (\frac{2 π}{365} t) = 11

Multiplicar ambos os lados por

10

12 + 3.5 sin (\frac{2 π}{365} t) = 11

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere is one digit to the right of the decimal point, therefore multiply by

10

12 \cdot 10 + 3.5 sin (\frac{2 π}{365} t) \cdot 10 = 11 \cdot 10

Simplificar

120 + 35 sin (\frac{2 π}{365} t) = 110

120 + 35 sin (\frac{2 π}{365} t) = 110

Mova

120

para o lado direito

120 + 35 sin (\frac{2 π}{365} t) = 110

Subtrair

120

de ambos os lados

120 + 35 sin (\frac{2 π}{365} t) - 120 = 110 - 120

Simplificar

35 sin (\frac{2 π}{365} t) = - 10

35 sin (\frac{2 π}{365} t) = - 10

Dividir ambos os lados por

35

35 sin (\frac{2 π}{365} t) = - 10

Dividir ambos os lados por

35

\frac{35 sin ( \frac{2 π}{365} t )}{35} = \frac{- 10}{35}

Simplificar

\frac{35 sin ( \frac{2 π}{365} t )}{35} = \frac{- 10}{35}

Simplificar

\frac{35 sin ( \frac{2 π}{365} t )}{35} : sin (\frac{2 π}{365} t)

\frac{35 sin ( \frac{2 π}{365} t )}{35}

Dividir:

\frac{35}{35} = 1

= sin (\frac{2 π}{365} t)

Simplificar

\frac{- 10}{35} : - \frac{2}{7}

\frac{- 10}{35}

Aplicar as propriedades das frações:

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

= - \frac{10}{35}

Eliminar o fator comum:

5

= - \frac{2}{7}

sin (\frac{2 π}{365} t) = - \frac{2}{7}

sin (\frac{2 π}{365} t) = - \frac{2}{7}

sin (\frac{2 π}{365} t) = - \frac{2}{7}

Aplique as propriedades trigonométricas inversas

sin (\frac{2 π}{365} t) = - \frac{2}{7}

Soluções gerais para

sin (\frac{2 π}{365} t) = - \frac{2}{7}

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

\frac{2 π}{365} t = arcsin (- \frac{2}{7}) + 2 πn, \frac{2 π}{365} t = π + arcsin (\frac{2}{7}) + 2 πn

\frac{2 π}{365} t = arcsin (- \frac{2}{7}) + 2 πn, \frac{2 π}{365} t = π + arcsin (\frac{2}{7}) + 2 πn

Resolver

\frac{2 π}{365} t = arcsin (- \frac{2}{7}) + 2 πn : t = - \frac{365 arcsin ( \frac{2}{7} )}{2 π} + 365 n

\frac{2 π}{365} t = arcsin (- \frac{2}{7}) + 2 πn

Simplificar

arcsin (- \frac{2}{7}) + 2 πn : - arcsin (\frac{2}{7}) + 2 πn

arcsin (- \frac{2}{7}) + 2 πn

Utilizar a seguinte propriedade:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{2}{7}) = - arcsin (\frac{2}{7})

= - arcsin (\frac{2}{7}) + 2 πn

\frac{2 π}{365} t = - arcsin (\frac{2}{7}) + 2 πn

Multiplicar ambos os lados por

365

\frac{2 π}{365} t = - arcsin (\frac{2}{7}) + 2 πn

Multiplicar ambos os lados por

365

365 \cdot \frac{2 π}{365} t = - 365 arcsin (\frac{2}{7}) + 365 \cdot 2 πn

Simplificar

365 \cdot \frac{2 π}{365} t = - 365 arcsin (\frac{2}{7}) + 365 \cdot 2 πn

Simplificar

365 \cdot \frac{2 π}{365} t : 2 π t

365 \cdot \frac{2 π}{365} t

Multiplicar frações:

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

= \frac{2 \cdot 365 π}{365} t

Eliminar o fator comum:

365

= t \cdot 2 π

Simplificar

- 365 arcsin (\frac{2}{7}) + 365 \cdot 2 πn : - 365 arcsin (\frac{2}{7}) + 730 πn

- 365 arcsin (\frac{2}{7}) + 365 \cdot 2 πn

Multiplicar os números:

365 \cdot 2 = 730

= - 365 arcsin (\frac{2}{7}) + 730 πn

2 π t = - 365 arcsin (\frac{2}{7}) + 730 πn

2 π t = - 365 arcsin (\frac{2}{7}) + 730 πn

2 π t = - 365 arcsin (\frac{2}{7}) + 730 πn

Dividir ambos os lados por

2 π

2 π t = - 365 arcsin (\frac{2}{7}) + 730 πn

Dividir ambos os lados por

2 π

\frac{2 π t}{2 π} = - \frac{365 arcsin ( \frac{2}{7} )}{2 π} + \frac{730 πn}{2 π}

Simplificar

\frac{2 π t}{2 π} = - \frac{365 arcsin ( \frac{2}{7} )}{2 π} + \frac{730 πn}{2 π}

Simplificar

\frac{2 π t}{2 π} : t

\frac{2 π t}{2 π}

Dividir:

\frac{2}{2} = 1

= \frac{π t}{π}

Eliminar o fator comum:

π

= t

Simplificar

- \frac{365 arcsin ( \frac{2}{7} )}{2 π} + \frac{730 πn}{2 π} : - \frac{365 arcsin ( \frac{2}{7} )}{2 π} + 365 n

- \frac{365 arcsin ( \frac{2}{7} )}{2 π} + \frac{730 πn}{2 π}

Cancelar

\frac{730 πn}{2 π} : 365 n

\frac{730 πn}{2 π}

Cancelar

\frac{730 πn}{2 π} : 365 n

\frac{730 πn}{2 π}

Dividir:

\frac{730}{2} = 365

= \frac{365 πn}{π}

Eliminar o fator comum:

π

= 365 n

= 365 n

= - \frac{365 arcsin ( \frac{2}{7} )}{2 π} + 365 n

t = - \frac{365 arcsin ( \frac{2}{7} )}{2 π} + 365 n

t = - \frac{365 arcsin ( \frac{2}{7} )}{2 π} + 365 n

t = - \frac{365 arcsin ( \frac{2}{7} )}{2 π} + 365 n

Resolver

\frac{2 π}{365} t = π + arcsin (\frac{2}{7}) + 2 πn : t = \frac{365}{2} + \frac{365 arcsin ( \frac{2}{7} )}{2 π} + 365 n

\frac{2 π}{365} t = π + arcsin (\frac{2}{7}) + 2 πn

Multiplicar ambos os lados por

365

\frac{2 π}{365} t = π + arcsin (\frac{2}{7}) + 2 πn

Multiplicar ambos os lados por

365

365 \cdot \frac{2 π}{365} t = 365 π + 365 arcsin (\frac{2}{7}) + 365 \cdot 2 πn

Simplificar

365 \cdot \frac{2 π}{365} t = 365 π + 365 arcsin (\frac{2}{7}) + 365 \cdot 2 πn

Simplificar

365 \cdot \frac{2 π}{365} t : 2 π t

365 \cdot \frac{2 π}{365} t

Multiplicar frações:

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

= \frac{2 \cdot 365 π}{365} t

Eliminar o fator comum:

365

= t \cdot 2 π

Simplificar

365 π + 365 arcsin (\frac{2}{7}) + 365 \cdot 2 πn : 365 π + 365 arcsin (\frac{2}{7}) + 730 πn

365 π + 365 arcsin (\frac{2}{7}) + 365 \cdot 2 πn

Multiplicar os números:

365 \cdot 2 = 730

= 365 π + 365 arcsin (\frac{2}{7}) + 730 πn

2 π t = 365 π + 365 arcsin (\frac{2}{7}) + 730 πn

2 π t = 365 π + 365 arcsin (\frac{2}{7}) + 730 πn

2 π t = 365 π + 365 arcsin (\frac{2}{7}) + 730 πn

Dividir ambos os lados por

2 π

2 π t = 365 π + 365 arcsin (\frac{2}{7}) + 730 πn

Dividir ambos os lados por

2 π

\frac{2 π t}{2 π} = \frac{365 π}{2 π} + \frac{365 arcsin ( \frac{2}{7} )}{2 π} + \frac{730 πn}{2 π}

Simplificar

\frac{2 π t}{2 π} = \frac{365 π}{2 π} + \frac{365 arcsin ( \frac{2}{7} )}{2 π} + \frac{730 πn}{2 π}

Simplificar

\frac{2 π t}{2 π} : t

\frac{2 π t}{2 π}

Dividir:

\frac{2}{2} = 1

= \frac{π t}{π}

Eliminar o fator comum:

π

= t

Simplificar

\frac{365 π}{2 π} + \frac{365 arcsin ( \frac{2}{7} )}{2 π} + \frac{730 πn}{2 π} : \frac{365}{2} + \frac{365 arcsin ( \frac{2}{7} )}{2 π} + 365 n

\frac{365 π}{2 π} + \frac{365 arcsin ( \frac{2}{7} )}{2 π} + \frac{730 πn}{2 π}

Cancelar

\frac{365 π}{2 π} : \frac{365}{2}

\frac{365 π}{2 π}

Eliminar o fator comum:

π

= \frac{365}{2}

= \frac{365}{2} + \frac{365 arcsin ( \frac{2}{7} )}{2 π} + \frac{730 πn}{2 π}

Cancelar

\frac{730 πn}{2 π} : 365 n

\frac{730 πn}{2 π}

Cancelar

\frac{730 πn}{2 π} : 365 n

\frac{730 πn}{2 π}

Dividir:

\frac{730}{2} = 365

= \frac{365 πn}{π}

Eliminar o fator comum:

π

= 365 n

= 365 n

= \frac{365}{2} + \frac{365 arcsin ( \frac{2}{7} )}{2 π} + 365 n

t = \frac{365}{2} + \frac{365 arcsin ( \frac{2}{7} )}{2 π} + 365 n

t = \frac{365}{2} + \frac{365 arcsin ( \frac{2}{7} )}{2 π} + 365 n

t = \frac{365}{2} + \frac{365 arcsin ( \frac{2}{7} )}{2 π} + 365 n

t = - \frac{365 arcsin ( \frac{2}{7} )}{2 π} + 365 n, t = \frac{365}{2} + \frac{365 arcsin ( \frac{2}{7} )}{2 π} + 365 n

Mostrar soluções na forma decimal

t = - \frac{365 \cdot 0.28975 \dots}{2 π} + 365 n, t = \frac{365}{2} + \frac{365 \cdot 0.28975 \dots}{2 π} + 365 n

Gráfico

Exemplos populares

sin(2t)=2sin(t)

sin (2 t) = 2 sin (t)

cos(α)=0

cos (α) = 0

solvefor x,cos(x^3y^3)=5y^3

so l v e f or x, cos (x^{3} y^{3}) = 5 y^{3}

cos^2(3/4 pi+x)+sin^2(7/4 pi-x)=1

cos^{2} (\frac{3}{4} π + x) + sin^{2} (\frac{7}{4} π - x) = 1

sin(4x)=-sin(x)

sin (4 x) = - sin (x)