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Popular >

sin^4(x)=sin^4(x)sec(x)

Solución

sin^{4} (x) = sin^{4} (x) sec (x)

Solución

x = 2 πn, x = π + 2 πn

+1

Grados

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

Pasos de solución

sin^{4} (x) = sin^{4} (x) sec (x)

Restar

sin^{4} (x) sec (x)

de ambos lados

sin^{4} (x) - sin^{4} (x) sec (x) = 0

Factorizar

sin^{4} (x) - sin^{4} (x) sec (x) : - sin^{4} (x) (sec (x) - 1)

sin^{4} (x) - sin^{4} (x) sec (x)

Factorizar el termino común

- sin^{4} (x)

= - sin^{4} (x) (- 1 + sec (x))

- sin^{4} (x) (sec (x) - 1) = 0

Resolver cada parte por separado

sin^{4} (x) = 0 or sec (x) - 1 = 0

sin^{4} (x) = 0 : x = 2 πn, x = π + 2 πn

sin^{4} (x) = 0

Utilizando el teorema de factor cero: si

ab = 0

entonces

a = 0

o

b = 0

sin (x) = 0

La solución es

sin (x) = 0

Soluciones generales para

sin (x) = 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}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

Resolver

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

sec (x) - 1 = 0 : x = 2 πn

sec (x) - 1 = 0

Mover

1

al lado derecho

sec (x) - 1 = 0

Sumar

1

a ambos lados

sec (x) - 1 + 1 = 0 + 1

Simplificar

sec (x) = 1

sec (x) = 1

Soluciones generales para

sec (x) = 1

sec (x)

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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

x = 0 + 2 πn

x = 0 + 2 πn

Resolver

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn

Combinar toda las soluciones

x = 2 πn, x = π + 2 πn

Gráfica

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