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Popular >

cos^2(a)= 2/3

Solución

cos^{2} (a) = \frac{2}{3}

Solución

a = 0.61547 \dots + 2 πn, a = 2 π - 0.61547 \dots + 2 πn, a = 2.52611 \dots + 2 πn, a = - 2.52611 \dots + 2 πn

+1

Grados

a = 35.26438 \dots^{\circ} + 36 0^{\circ} n, a = 324.73561 \dots^{\circ} + 36 0^{\circ} n, a = 144.73561 \dots^{\circ} + 36 0^{\circ} n, a = - 144.73561 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

cos^{2} (a) = \frac{2}{3}

Usando el método de sustitución

cos^{2} (a) = \frac{2}{3}

Sea:

cos (a) = u

u^{2} = \frac{2}{3}

u^{2} = \frac{2}{3} : u = \frac{2}{3}, u = - \frac{2}{3}

u^{2} = \frac{2}{3}

Para

x^{2} = f (a)

las soluciones son

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

u = \frac{2}{3}, u = - \frac{2}{3}

Sustituir en la ecuación

u = cos (a)

cos (a) = \frac{2}{3}, cos (a) = - \frac{2}{3}

cos (a) = \frac{2}{3}, cos (a) = - \frac{2}{3}

cos (a) = \frac{2}{3} : a = arccos (\frac{2}{3}) + 2 πn, a = 2 π - arccos (\frac{2}{3}) + 2 πn

cos (a) = \frac{2}{3}

Aplicar propiedades trigonométricas inversas

cos (a) = \frac{2}{3}

Soluciones generales para

cos (a) = \frac{2}{3}

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

a = arccos (\frac{2}{3}) + 2 πn, a = 2 π - arccos (\frac{2}{3}) + 2 πn

a = arccos (\frac{2}{3}) + 2 πn, a = 2 π - arccos (\frac{2}{3}) + 2 πn

cos (a) = - \frac{2}{3} : a = arccos (- \frac{2}{3}) + 2 πn, a = - arccos (- \frac{2}{3}) + 2 πn

cos (a) = - \frac{2}{3}

Aplicar propiedades trigonométricas inversas

cos (a) = - \frac{2}{3}

Soluciones generales para

cos (a) = - \frac{2}{3}

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

a = arccos (- \frac{2}{3}) + 2 πn, a = - arccos (- \frac{2}{3}) + 2 πn

a = arccos (- \frac{2}{3}) + 2 πn, a = - arccos (- \frac{2}{3}) + 2 πn

Combinar toda las soluciones

a = arccos (\frac{2}{3}) + 2 πn, a = 2 π - arccos (\frac{2}{3}) + 2 πn, a = arccos (- \frac{2}{3}) + 2 πn, a = - arccos (- \frac{2}{3}) + 2 πn

Mostrar soluciones en forma decimal

a = 0.61547 \dots + 2 πn, a = 2 π - 0.61547 \dots + 2 πn, a = 2.52611 \dots + 2 πn, a = - 2.52611 \dots + 2 πn

Ejemplos populares

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sin (2 x) = - 0.848055484

2+cos^2(x)=3cos(x)

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cos (x + 4 0^{\circ}) = 0.85

sin^2(a)=1-cos(2a)

sin^{2} (a) = 1 - cos (2 a)

cos^4(x)=cos^2(x)

cos^{4} (x) = cos^{2} (x)