English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Trigonometría >

105=100+30sin((12pi)/5 t)

Solución

105 = 100 + 30 sin (\frac{12 π}{5} t)

Solución

t = \frac{5 \cdot 0.16744 \dots}{12 π} + \frac{5 n}{6}, t = \frac{5}{12} - \frac{5 \cdot 0.16744 \dots}{12 π} + \frac{5 n}{6}

Grados

t = 1.27245 \dots^{\circ} + 47.74648 \dots^{\circ} n, t = 22.60078 \dots^{\circ} + 47.74648 \dots^{\circ} n

Pasos de solución

105 = 100 + 30 sin (\frac{12 π}{5} t)

Intercambiar lados

100 + 30 sin (\frac{12 π}{5} t) = 105

Desplace

100

a la derecha

100 + 30 sin (\frac{12 π}{5} t) = 105

Restar

100

de ambos lados

100 + 30 sin (\frac{12 π}{5} t) - 100 = 105 - 100

Simplificar

30 sin (\frac{12 π}{5} t) = 5

30 sin (\frac{12 π}{5} t) = 5

Dividir ambos lados entre

30

30 sin (\frac{12 π}{5} t) = 5

Dividir ambos lados entre

30

\frac{30 sin ( \frac{12 π}{5} t )}{30} = \frac{5}{30}

Simplificar

sin (\frac{12 π}{5} t) = \frac{1}{6}

sin (\frac{12 π}{5} t) = \frac{1}{6}

Aplicar propiedades trigonométricas inversas

sin (\frac{12 π}{5} t) = \frac{1}{6}

Soluciones generales para

sin (\frac{12 π}{5} t) = \frac{1}{6}

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

\frac{12 π}{5} t = arcsin (\frac{1}{6}) + 2 πn, \frac{12 π}{5} t = π - arcsin (\frac{1}{6}) + 2 πn

\frac{12 π}{5} t = arcsin (\frac{1}{6}) + 2 πn, \frac{12 π}{5} t = π - arcsin (\frac{1}{6}) + 2 πn

Resolver

\frac{12 π}{5} t = arcsin (\frac{1}{6}) + 2 πn : t = \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{5 n}{6}

\frac{12 π}{5} t = arcsin (\frac{1}{6}) + 2 πn

Multiplicar ambos lados por

5

\frac{12 π}{5} t = arcsin (\frac{1}{6}) + 2 πn

Multiplicar ambos lados por

5

5 \cdot \frac{12 π}{5} t = 5 arcsin (\frac{1}{6}) + 5 \cdot 2 πn

Simplificar

5 \cdot \frac{12 π}{5} t = 5 arcsin (\frac{1}{6}) + 5 \cdot 2 πn

Simplificar

5 \cdot \frac{12 π}{5} t : 12 π t

5 \cdot \frac{12 π}{5} t

Multiplicar fracciones:

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

= \frac{12 \cdot 5 π}{5} t

Eliminar los terminos comunes:

5

= t \cdot 12 π

Simplificar

5 arcsin (\frac{1}{6}) + 5 \cdot 2 πn : 5 arcsin (\frac{1}{6}) + 10 πn

5 arcsin (\frac{1}{6}) + 5 \cdot 2 πn

Multiplicar los numeros:

5 \cdot 2 = 10

= 5 arcsin (\frac{1}{6}) + 10 πn

12 π t = 5 arcsin (\frac{1}{6}) + 10 πn

12 π t = 5 arcsin (\frac{1}{6}) + 10 πn

12 π t = 5 arcsin (\frac{1}{6}) + 10 πn

Dividir ambos lados entre

12 π

12 π t = 5 arcsin (\frac{1}{6}) + 10 πn

Dividir ambos lados entre

12 π

\frac{12 π t}{12 π} = \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{10 πn}{12 π}

Simplificar

\frac{12 π t}{12 π} = \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{10 πn}{12 π}

Simplificar

\frac{12 π t}{12 π} : t

\frac{12 π t}{12 π}

Dividir:

\frac{12}{12} = 1

= \frac{π t}{π}

Eliminar los terminos comunes:

π

= t

Simplificar

\frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{10 πn}{12 π} : \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{5 n}{6}

\frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{10 πn}{12 π}

Cancelar

\frac{10 πn}{12 π} : \frac{5 n}{6}

\frac{10 πn}{12 π}

Cancelar

\frac{10 πn}{12 π} : \frac{5 n}{6}

\frac{10 πn}{12 π}

Eliminar los terminos comunes:

2

= \frac{5 πn}{6 π}

Eliminar los terminos comunes:

π

= \frac{5 n}{6}

= \frac{5 n}{6}

= \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{5 n}{6}

t = \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{5 n}{6}

t = \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{5 n}{6}

t = \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{5 n}{6}

Resolver

\frac{12 π}{5} t = π - arcsin (\frac{1}{6}) + 2 πn : t = \frac{5}{12} - \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{5 n}{6}

\frac{12 π}{5} t = π - arcsin (\frac{1}{6}) + 2 πn

Multiplicar ambos lados por

5

\frac{12 π}{5} t = π - arcsin (\frac{1}{6}) + 2 πn

Multiplicar ambos lados por

5

5 \cdot \frac{12 π}{5} t = 5 π - 5 arcsin (\frac{1}{6}) + 5 \cdot 2 πn

Simplificar

5 \cdot \frac{12 π}{5} t = 5 π - 5 arcsin (\frac{1}{6}) + 5 \cdot 2 πn

Simplificar

5 \cdot \frac{12 π}{5} t : 12 π t

5 \cdot \frac{12 π}{5} t

Multiplicar fracciones:

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

= \frac{12 \cdot 5 π}{5} t

Eliminar los terminos comunes:

5

= t \cdot 12 π

Simplificar

5 π - 5 arcsin (\frac{1}{6}) + 5 \cdot 2 πn : 5 π - 5 arcsin (\frac{1}{6}) + 10 πn

5 π - 5 arcsin (\frac{1}{6}) + 5 \cdot 2 πn

Multiplicar los numeros:

5 \cdot 2 = 10

= 5 π - 5 arcsin (\frac{1}{6}) + 10 πn

12 π t = 5 π - 5 arcsin (\frac{1}{6}) + 10 πn

12 π t = 5 π - 5 arcsin (\frac{1}{6}) + 10 πn

12 π t = 5 π - 5 arcsin (\frac{1}{6}) + 10 πn

Dividir ambos lados entre

12 π

12 π t = 5 π - 5 arcsin (\frac{1}{6}) + 10 πn

Dividir ambos lados entre

12 π

\frac{12 π t}{12 π} = \frac{5 π}{12 π} - \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{10 πn}{12 π}

Simplificar

\frac{12 π t}{12 π} = \frac{5 π}{12 π} - \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{10 πn}{12 π}

Simplificar

\frac{12 π t}{12 π} : t

\frac{12 π t}{12 π}

Dividir:

\frac{12}{12} = 1

= \frac{π t}{π}

Eliminar los terminos comunes:

π

= t

Simplificar

\frac{5 π}{12 π} - \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{10 πn}{12 π} : \frac{5}{12} - \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{5 n}{6}

\frac{5 π}{12 π} - \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{10 πn}{12 π}

Cancelar

\frac{5 π}{12 π} : \frac{5}{12}

\frac{5 π}{12 π}

Eliminar los terminos comunes:

π

= \frac{5}{12}

= \frac{5}{12} - \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{10 πn}{12 π}

Cancelar

\frac{10 πn}{12 π} : \frac{5 n}{6}

\frac{10 πn}{12 π}

Cancelar

\frac{10 πn}{12 π} : \frac{5 n}{6}

\frac{10 πn}{12 π}

Eliminar los terminos comunes:

2

= \frac{5 πn}{6 π}

Eliminar los terminos comunes:

π

= \frac{5 n}{6}

= \frac{5 n}{6}

= \frac{5}{12} - \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{5 n}{6}

t = \frac{5}{12} - \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{5 n}{6}

t = \frac{5}{12} - \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{5 n}{6}

t = \frac{5}{12} - \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{5 n}{6}

t = \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{5 n}{6}, t = \frac{5}{12} - \frac{5 arcsin ( \frac{1}{6} )}{12 π} + \frac{5 n}{6}

Mostrar soluciones en forma decimal

t = \frac{5 \cdot 0.16744 \dots}{12 π} + \frac{5 n}{6}, t = \frac{5}{12} - \frac{5 \cdot 0.16744 \dots}{12 π} + \frac{5 n}{6}

Gráfica

Ejemplos populares

3/(sin(x))= 1/(cos(x))