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Popular >

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

Solución

100 = 100 + 30 sin (\frac{12 π}{5} t)

Solución

t = \frac{5 n}{6}, t = \frac{5}{12} + \frac{5 n}{6}

Grados

t = 0^{\circ} + 47.74648 \dots^{\circ} n, t = 23.87324 \dots^{\circ} + 47.74648 \dots^{\circ} n

Pasos de solución

100 = 100 + 30 sin (\frac{12 π}{5} t)

Intercambiar lados

100 + 30 sin (\frac{12 π}{5} t) = 100

Restar

100

de ambos lados

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

Simplificar

30 sin (\frac{12 π}{5} t) = 0

Dividir ambos lados entre

30

30 sin (\frac{12 π}{5} t) = 0

Dividir ambos lados entre

30

\frac{30 sin ( \frac{12 π}{5} t )}{30} = \frac{0}{30}

Simplificar

sin (\frac{12 π}{5} t) = 0

sin (\frac{12 π}{5} t) = 0

Soluciones generales para

sin (\frac{12 π}{5} t) = 0

tabla de valores periódicos con

2 πn

intervalos:

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{12 π}{5} t = 0 + 2 πn, \frac{12 π}{5} t = π + 2 πn

\frac{12 π}{5} t = 0 + 2 πn, \frac{12 π}{5} t = π + 2 πn

Resolver

\frac{12 π}{5} t = 0 + 2 πn : t = \frac{5 n}{6}

\frac{12 π}{5} t = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{12 π}{5} t = 2 πn

Multiplicar ambos lados por

5

\frac{12 π}{5} t = 2 πn

Multiplicar ambos lados por

5

5 \cdot \frac{12 π}{5} t = 5 \cdot 2 πn

Simplificar

12 π t = 10 πn

12 π t = 10 πn

Dividir ambos lados entre

12 π

12 π t = 10 πn

Dividir ambos lados entre

12 π

\frac{12 π t}{12 π} = \frac{10 πn}{12 π}

Simplificar

\frac{12 π t}{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{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}

t = \frac{5 n}{6}

t = \frac{5 n}{6}

t = \frac{5 n}{6}

Resolver

\frac{12 π}{5} t = π + 2 πn : t = \frac{5}{12} + \frac{5 n}{6}

\frac{12 π}{5} t = π + 2 πn

Multiplicar ambos lados por

5

\frac{12 π}{5} t = π + 2 πn

Multiplicar ambos lados por

5

5 \cdot \frac{12 π}{5} t = 5 π + 5 \cdot 2 πn

Simplificar

12 π t = 5 π + 10 πn

12 π t = 5 π + 10 πn

Dividir ambos lados entre

12 π

12 π t = 5 π + 10 πn

Dividir ambos lados entre

12 π

\frac{12 π t}{12 π} = \frac{5 π}{12 π} + \frac{10 πn}{12 π}

Simplificar

\frac{12 π t}{12 π} = \frac{5 π}{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{10 πn}{12 π} : \frac{5}{12} + \frac{5 n}{6}

\frac{5 π}{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{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 n}{6}

t = \frac{5}{12} + \frac{5 n}{6}

t = \frac{5}{12} + \frac{5 n}{6}

t = \frac{5}{12} + \frac{5 n}{6}

t = \frac{5 n}{6}, t = \frac{5}{12} + \frac{5 n}{6}

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\frac{sin ( 12 0 ^{\circ} )}{2.34} = \frac{sin ( θ )}{1.2}

tan(x)= 12/50

tan (x) = \frac{12}{50}

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