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sin(4(x-pi/4))=0

Solución

sin (4 (x - \frac{π}{4})) = 0

Solución

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

Grados

x = 4 5^{\circ} + 9 0^{\circ} n, x = 9 0^{\circ} + 9 0^{\circ} n

Pasos de solución

sin (4 (x - \frac{π}{4})) = 0

Soluciones generales para

sin (4 (x - \frac{π}{4})) = 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}

4 (x - \frac{π}{4}) = 0 + 2 πn, 4 (x - \frac{π}{4}) = π + 2 πn

4 (x - \frac{π}{4}) = 0 + 2 πn, 4 (x - \frac{π}{4}) = π + 2 πn

Resolver

4 (x - \frac{π}{4}) = 0 + 2 πn : x = \frac{πn}{2} + \frac{π}{4}

4 (x - \frac{π}{4}) = 0 + 2 πn

0 + 2 πn = 2 πn

4 (x - \frac{π}{4}) = 2 πn

Dividir ambos lados entre

4

4 (x - \frac{π}{4}) = 2 πn

Dividir ambos lados entre

4

\frac{4 ( x - \frac{π}{4} )}{4} = \frac{2 πn}{4}

Simplificar

x - \frac{π}{4} = \frac{πn}{2}

x - \frac{π}{4} = \frac{πn}{2}

Mover

\frac{π}{4}

al lado derecho

x - \frac{π}{4} = \frac{πn}{2}

Sumar

\frac{π}{4}

a ambos lados

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

Simplificar

x = \frac{πn}{2} + \frac{π}{4}

x = \frac{πn}{2} + \frac{π}{4}

Resolver

4 (x - \frac{π}{4}) = π + 2 πn : x = \frac{π + πn}{2}

4 (x - \frac{π}{4}) = π + 2 πn

Dividir ambos lados entre

4

4 (x - \frac{π}{4}) = π + 2 πn

Dividir ambos lados entre

4

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

Simplificar

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

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

Mover

\frac{π}{4}

al lado derecho

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

Sumar

\frac{π}{4}

a ambos lados

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

Simplificar

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

Simplificar

x - \frac{π}{4} + \frac{π}{4} : x

x - \frac{π}{4} + \frac{π}{4}

Sumar elementos similares:

- \frac{π}{4} + \frac{π}{4} = 0

= x

Simplificar

\frac{π}{4} + \frac{πn}{2} + \frac{π}{4} : \frac{π + πn}{2}

\frac{π}{4} + \frac{πn}{2} + \frac{π}{4}

Agrupar términos semejantes

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

Combinar las fracciones usando el mínimo común denominador:

\frac{π}{2}

Aplicar la regla

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

= \frac{π + π}{4}

Sumar elementos similares:

π + π = 2 π

= \frac{2 π}{4}

Eliminar los terminos comunes:

2

= \frac{π}{2}

= \frac{π}{2} + \frac{πn}{2}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{π + πn}{2}

x = \frac{π + πn}{2}

x = \frac{π + πn}{2}

x = \frac{π + πn}{2}

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

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3 arcsin (2 θ) = 2 π

cos^3(x)+cos^2(x)-cos(x)-1=0

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tan (2 θ) = 1, 0^{\circ} \leq θ \leq 36 0^{\circ}

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