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sin(62.8x+pi/4)=sin(pi/4)

Solución

sin (62.8 x + \frac{π}{4}) = sin (\frac{π}{4})

Solución

x = \frac{5 πn}{157}, x = \frac{5 πn}{157} + \frac{5 π}{628}

Grados

x = 0^{\circ} + 5.73248 \dots^{\circ} n, x = 1.43312 \dots^{\circ} + 5.73248 \dots^{\circ} n

Pasos de solución

sin (62.8 x + \frac{π}{4}) = sin (\frac{π}{4})

sin (\frac{π}{4}) = \frac{2}{2}

sin (\frac{π}{4})

Utilizar la siguiente identidad trivial:

sin (\frac{π}{4}) = \frac{2}{2}

sin (\frac{π}{4})

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{2}{2}

= \frac{2}{2}

sin (62.8 x + \frac{π}{4}) = \frac{2}{2}

Soluciones generales para

sin (62.8 x + \frac{π}{4}) = \frac{2}{2}

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}

62.8 x + \frac{π}{4} = \frac{π}{4} + 2 πn, 62.8 x + \frac{π}{4} = \frac{3 π}{4} + 2 πn

62.8 x + \frac{π}{4} = \frac{π}{4} + 2 πn, 62.8 x + \frac{π}{4} = \frac{3 π}{4} + 2 πn

Resolver

62.8 x + \frac{π}{4} = \frac{π}{4} + 2 πn : x = \frac{5 πn}{157}

62.8 x + \frac{π}{4} = \frac{π}{4} + 2 πn

Restar

\frac{π}{4}

de ambos lados

62.8 x + \frac{π}{4} - \frac{π}{4} = \frac{π}{4} + 2 πn - \frac{π}{4}

Simplificar

62.8 x = 2 πn

Multiplicar ambos lados por

10

62.8 x = 2 πn

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

62.8 x \cdot 10 = 2 πn \cdot 10

Simplificar

628 x = 20 πn

628 x = 20 πn

Dividir ambos lados entre

628

628 x = 20 πn

Dividir ambos lados entre

628

\frac{628 x}{628} = \frac{20 πn}{628}

Simplificar

x = \frac{5 πn}{157}

x = \frac{5 πn}{157}

Resolver

62.8 x + \frac{π}{4} = \frac{3 π}{4} + 2 πn : x = \frac{5 πn}{157} + \frac{5 π}{628}

62.8 x + \frac{π}{4} = \frac{3 π}{4} + 2 πn

Multiplicar ambos lados por

10

62.8 x + \frac{π}{4} = \frac{3 π}{4} + 2 πn

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

62.8 x \cdot 10 + \frac{π}{4} \cdot 10 = \frac{3 π}{4} \cdot 10 + 2 πn \cdot 10

Simplificar

628 x + \frac{5 π}{2} = \frac{15 π}{2} + 20 πn

628 x + \frac{5 π}{2} = \frac{15 π}{2} + 20 πn

Mover

\frac{5 π}{2}

al lado derecho

628 x + \frac{5 π}{2} = \frac{15 π}{2} + 20 πn

Restar

\frac{5 π}{2}

de ambos lados

628 x + \frac{5 π}{2} - \frac{5 π}{2} = \frac{15 π}{2} + 20 πn - \frac{5 π}{2}

Simplificar

628 x + \frac{5 π}{2} - \frac{5 π}{2} = \frac{15 π}{2} + 20 πn - \frac{5 π}{2}

Simplificar

628 x + \frac{5 π}{2} - \frac{5 π}{2} : 628 x

628 x + \frac{5 π}{2} - \frac{5 π}{2}

Sumar elementos similares:

\frac{5 π}{2} - \frac{5 π}{2} = 0

= 628 x

Simplificar

\frac{15 π}{2} + 20 πn - \frac{5 π}{2} : 20 πn + 5 π

\frac{15 π}{2} + 20 πn - \frac{5 π}{2}

Agrupar términos semejantes

= 20 πn - \frac{5 π}{2} + \frac{15 π}{2}

Combinar las fracciones usando el mínimo común denominador:

5 π

Aplicar la regla

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

= \frac{- 5 π + 15 π}{2}

Sumar elementos similares:

- 5 π + 15 π = 10 π

= \frac{10 π}{2}

Dividir:

\frac{10}{2} = 5

= 5 π

= 20 πn + 5 π

628 x = 20 πn + 5 π

628 x = 20 πn + 5 π

628 x = 20 πn + 5 π

Dividir ambos lados entre

628

628 x = 20 πn + 5 π

Dividir ambos lados entre

628

\frac{628 x}{628} = \frac{20 πn}{628} + \frac{5 π}{628}

Simplificar

x = \frac{5 πn}{157} + \frac{5 π}{628}

x = \frac{5 πn}{157} + \frac{5 π}{628}

x = \frac{5 πn}{157}, x = \frac{5 πn}{157} + \frac{5 π}{628}

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