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Popular >

cos^2(x)-sin^2(x)=-3/4

Solución

cos^{2} (x) - sin^{2} (x) = - \frac{3}{4}

x = \frac{2.41885 \dots}{2} + πn, x = - \frac{2.41885 \dots}{2} + πn

Grados

x = 69.29518 \dots^{\circ} + 18 0^{\circ} n, x = - 69.29518 \dots^{\circ} + 18 0^{\circ} n

Pasos de solución

cos^{2} (x) - sin^{2} (x) = - \frac{3}{4}

Re-escribir usando identidades trigonométricas

cos^{2} (x) - sin^{2} (x)

Utilizar la identidad trigonométrica del ángulo doble:

cos^{2} (x) - sin^{2} (x) = cos (2 x)

= cos (2 x)

cos (2 x) = - \frac{3}{4}

Aplicar propiedades trigonométricas inversas

cos (2 x) = - \frac{3}{4}

Soluciones generales para

cos (2 x) = - \frac{3}{4}

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

2 x = arccos (- \frac{3}{4}) + 2 πn, 2 x = - arccos (- \frac{3}{4}) + 2 πn

2 x = arccos (- \frac{3}{4}) + 2 πn, 2 x = - arccos (- \frac{3}{4}) + 2 πn

Resolver

2 x = arccos (- \frac{3}{4}) + 2 πn : x = \frac{arccos ( - \frac{3}{4} )}{2} + πn

2 x = arccos (- \frac{3}{4}) + 2 πn

Dividir ambos lados entre

2

2 x = arccos (- \frac{3}{4}) + 2 πn

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{arccos ( - \frac{3}{4} )}{2} + \frac{2 πn}{2}

Simplificar

x = \frac{arccos ( - \frac{3}{4} )}{2} + πn

x = \frac{arccos ( - \frac{3}{4} )}{2} + πn

Resolver

2 x = - arccos (- \frac{3}{4}) + 2 πn : x = - \frac{arccos ( - \frac{3}{4} )}{2} + πn

2 x = - arccos (- \frac{3}{4}) + 2 πn

Dividir ambos lados entre

2

2 x = - arccos (- \frac{3}{4}) + 2 πn

Dividir ambos lados entre

2

\frac{2 x}{2} = - \frac{arccos ( - \frac{3}{4} )}{2} + \frac{2 πn}{2}

Simplificar

x = - \frac{arccos ( - \frac{3}{4} )}{2} + πn

x = - \frac{arccos ( - \frac{3}{4} )}{2} + πn

x = \frac{arccos ( - \frac{3}{4} )}{2} + πn, x = - \frac{arccos ( - \frac{3}{4} )}{2} + πn

Mostrar soluciones en forma decimal

x = \frac{2.41885 \dots}{2} + πn, x = - \frac{2.41885 \dots}{2} + πn

8 cos (8 x) = 0

sin (x) = 22

sin (x) (1 + sin (x)) = 0

cos (x) = 10

cos^{2} (x) - 7 cos (x) + 12 = 0