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solvefor x, 1/6 =cos^2(x)

Solución

resolver para

x, \frac{1}{6} = cos^{2} (x)

Solución

x = 1.15026 \dots + 2 πn, x = 2 π - 1.15026 \dots + 2 πn, x = 1.99133 \dots + 2 πn, x = - 1.99133 \dots + 2 πn

+1

Grados

x = 65.90515 \dots^{\circ} + 36 0^{\circ} n, x = 294.09484 \dots^{\circ} + 36 0^{\circ} n, x = 114.09484 \dots^{\circ} + 36 0^{\circ} n, x = - 114.09484 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

\frac{1}{6} = cos^{2} (x)

Intercambiar lados

cos^{2} (x) = \frac{1}{6}

Usando el método de sustitución

cos^{2} (x) = \frac{1}{6}

Sea:

cos (x) = u

u^{2} = \frac{1}{6}

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

u^{2} = \frac{1}{6}

Para

x^{2} = f (a)

las soluciones son

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

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

Sustituir en la ecuación

u = cos (x)

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

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

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

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

Aplicar propiedades trigonométricas inversas

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

Soluciones generales para

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

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

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

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

cos (x) = - \frac{1}{6} : x = arccos (- \frac{1}{6}) + 2 πn, x = - arccos (- \frac{1}{6}) + 2 πn

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

Aplicar propiedades trigonométricas inversas

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

Soluciones generales para

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

cos (x) = - a \Rightarrow x = arccos (- a) + 2 πn, x = - arccos (- a) + 2 πn

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

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

Combinar toda las soluciones

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

Mostrar soluciones en forma decimal

x = 1.15026 \dots + 2 πn, x = 2 π - 1.15026 \dots + 2 πn, x = 1.99133 \dots + 2 πn, x = - 1.99133 \dots + 2 πn

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