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Popular >

sec^2(x)=9

Solución

sec^{2} (x) = 9

Solución

x = 1.23095 \dots + 2 πn, x = 2 π - 1.23095 \dots + 2 πn, x = 1.91063 \dots + 2 πn, x = - 1.91063 \dots + 2 πn

+1

Grados

x = 70.52877 \dots^{\circ} + 36 0^{\circ} n, x = 289.47122 \dots^{\circ} + 36 0^{\circ} n, x = 109.47122 \dots^{\circ} + 36 0^{\circ} n, x = - 109.47122 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

sec^{2} (x) = 9

Usando el método de sustitución

sec^{2} (x) = 9

Sea:

sec (x) = u

u^{2} = 9

u^{2} = 9 : u = 3, u = - 3

u^{2} = 9

Para

x^{2} = f (a)

las soluciones son

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

u = 9, u = - 9

9 = 3

9

Descomponer el número en factores primos:

9 = 3^{2}

= 3^{2}

Aplicar las leyes de los exponentes:

3^{2} = 3

= 3

- 9 = - 3

- 9

9 = 3

9

Descomponer el número en factores primos:

9 = 3^{2}

= 3^{2}

Aplicar las leyes de los exponentes:

3^{2} = 3

= 3

= - 3

u = 3, u = - 3

Sustituir en la ecuación

u = sec (x)

sec (x) = 3, sec (x) = - 3

sec (x) = 3, sec (x) = - 3

sec (x) = 3 : x = arcsec (3) + 2 πn, x = 2 π - arcsec (3) + 2 πn

sec (x) = 3

Aplicar propiedades trigonométricas inversas

sec (x) = 3

Soluciones generales para

sec (x) = 3

sec (x) = a \Rightarrow x = arcsec (a) + 2 πn, x = 2 π - arcsec (a) + 2 πn

x = arcsec (3) + 2 πn, x = 2 π - arcsec (3) + 2 πn

x = arcsec (3) + 2 πn, x = 2 π - arcsec (3) + 2 πn

sec (x) = - 3 : x = arcsec (- 3) + 2 πn, x = - arcsec (- 3) + 2 πn

sec (x) = - 3

Aplicar propiedades trigonométricas inversas

sec (x) = - 3

Soluciones generales para

sec (x) = - 3

sec (x) = - a \Rightarrow x = arcsec (- a) + 2 πn, x = - arcsec (- a) + 2 πn

x = arcsec (- 3) + 2 πn, x = - arcsec (- 3) + 2 πn

x = arcsec (- 3) + 2 πn, x = - arcsec (- 3) + 2 πn

Combinar toda las soluciones

x = arcsec (3) + 2 πn, x = 2 π - arcsec (3) + 2 πn, x = arcsec (- 3) + 2 πn, x = - arcsec (- 3) + 2 πn

Mostrar soluciones en forma decimal

x = 1.23095 \dots + 2 πn, x = 2 π - 1.23095 \dots + 2 πn, x = 1.91063 \dots + 2 πn, x = - 1.91063 \dots + 2 πn

Ejemplos populares

4cos^2(x)-3=0,0<= x<2pi

4 cos^{2} (x) - 3 = 0, 0 \leq x < 2 π

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

\frac{1}{cos ^{2} ( x )} = \frac{2}{3 - 3 sin ( x )}

cos (4 x) = - 1

0.94=0.33sin(x)+cos(x)

0.94 = 0.33 sin (x) + cos (x)

cos (\frac{x}{2}) = - \frac{1}{2}