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sin^2(x)= 1/36

Solución

sin^{2} (x) = \frac{1}{36}

Solución

x = 0.16744 \dots + 2 πn, x = π - 0.16744 \dots + 2 πn, x = - 0.16744 \dots + 2 πn, x = π + 0.16744 \dots + 2 πn

+1

Grados

x = 9.59406 \dots^{\circ} + 36 0^{\circ} n, x = 170.40593 \dots^{\circ} + 36 0^{\circ} n, x = - 9.59406 \dots^{\circ} + 36 0^{\circ} n, x = 189.59406 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

sin^{2} (x) = \frac{1}{36}

Usando el método de sustitución

sin^{2} (x) = \frac{1}{36}

Sea:

sin (x) = u

u^{2} = \frac{1}{36}

u^{2} = \frac{1}{36} : u = \frac{1}{6}, u = - \frac{1}{6}

u^{2} = \frac{1}{36}

Para

x^{2} = f (a)

las soluciones son

x = f (a), - f (a)

u = \frac{1}{36}, u = - \frac{1}{36}

\frac{1}{36} = \frac{1}{6}

\frac{1}{36}

Aplicar la siguiente propiedad de los radicales:

asumiendo que

a \geq 0, b \geq 0

= \frac{1}{36}

36 = 6

36

Descomponer el número en factores primos:

36 = 6^{2}

= 6^{2}

Aplicar las leyes de los exponentes:

6^{2} = 6

= 6

= \frac{1}{6}

Aplicar la regla

1 = 1

= \frac{1}{6}

- \frac{1}{36} = - \frac{1}{6}

- \frac{1}{36}

Simplificar

\frac{1}{36} : \frac{1}{6}

\frac{1}{36}

Aplicar la siguiente propiedad de los radicales:

asumiendo que

a \geq 0, b \geq 0

= \frac{1}{36}

36 = 6

36

Descomponer el número en factores primos:

36 = 6^{2}

= 6^{2}

Aplicar las leyes de los exponentes:

6^{2} = 6

= 6

= \frac{1}{6}

= - \frac{1}{6}

Aplicar la regla

1 = 1

= - \frac{1}{6}

u = \frac{1}{6}, u = - \frac{1}{6}

Sustituir en la ecuación

u = sin (x)

sin (x) = \frac{1}{6}, sin (x) = - \frac{1}{6}

sin (x) = \frac{1}{6}, sin (x) = - \frac{1}{6}

sin (x) = \frac{1}{6} : x = arcsin (\frac{1}{6}) + 2 πn, x = π - arcsin (\frac{1}{6}) + 2 πn

sin (x) = \frac{1}{6}

Aplicar propiedades trigonométricas inversas

sin (x) = \frac{1}{6}

Soluciones generales para

sin (x) = \frac{1}{6}

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

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

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

sin (x) = - \frac{1}{6} : x = arcsin (- \frac{1}{6}) + 2 πn, x = π + arcsin (\frac{1}{6}) + 2 πn

sin (x) = - \frac{1}{6}

Aplicar propiedades trigonométricas inversas

sin (x) = - \frac{1}{6}

Soluciones generales para

sin (x) = - \frac{1}{6}

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

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

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

Combinar toda las soluciones

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

Mostrar soluciones en forma decimal

x = 0.16744 \dots + 2 πn, x = π - 0.16744 \dots + 2 πn, x = - 0.16744 \dots + 2 πn, x = π + 0.16744 \dots + 2 πn

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