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Popular Trigonometría >

(sin^2(x))/(1-cos(x))=1.23

Solución

\frac{sin ^{2} ( x )}{1 - cos ( x )} = 1.23

Solución

x = 1.33871 \dots + 2 πn, x = 2 π - 1.33871 \dots + 2 πn

Grados

x = 76.70292 \dots^{\circ} + 36 0^{\circ} n, x = 283.29707 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

\frac{sin ^{2} ( x )}{1 - cos ( x )} = 1.23

Restar

1.23

de ambos lados

\frac{sin ^{2} ( x )}{1 - cos ( x )} - 1.23 = 0

Re-escribir usando identidades trigonométricas

- 1.23 + \frac{sin ^{2} ( x )}{1 - cos ( x )}

Utilizar la identidad pitagórica:

cos^{2} (x) + sin^{2} (x) = 1

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

= - 1.23 + \frac{1 - cos ^{2} ( x )}{1 - cos ( x )}

Simplificar

- 1.23 + \frac{1 - cos ^{2} ( x )}{1 - cos ( x )} : cos (x) - 0.23

- 1.23 + \frac{1 - cos ^{2} ( x )}{1 - cos ( x )}

Cancelar

\frac{1 - cos ^{2} ( x )}{1 - cos ( x )} : cos (x) + 1

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

Factorizar

1 - cos^{2} (x) : - (cos (x) + 1) (cos (x) - 1)

1 - cos^{2} (x)

Factorizar el termino común

- 1

= - (cos^{2} (x) - 1)

Factorizar

cos^{2} (x) - 1 : (cos (x) + 1) (cos (x) - 1)

cos^{2} (x) - 1

Reescribir

1

como

1^{2}

= cos^{2} (x) - 1^{2}

Aplicar la siguiente regla para binomios al cuadrado:

x^{2} - y^{2} = (x + y) (x - y)

cos^{2} (x) - 1^{2} = (cos (x) + 1) (cos (x) - 1)

= (cos (x) + 1) (cos (x) - 1)

= - (cos (x) + 1) (cos (x) - 1)

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

Cancelar

- \frac{( cos ( x ) + 1 ) ( cos ( x ) - 1 )}{1 - cos ( x )} : cos (x) + 1

- \frac{( cos ( x ) + 1 ) ( cos ( x ) - 1 )}{1 - cos ( x )}

- cos (x) + 1 = - (cos (x) - 1)

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

Simplificar

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

Eliminar los terminos comunes:

cos (x) - 1

= cos (x) + 1

= cos (x) + 1

= - 1.23 + cos (x) + 1

Agrupar términos semejantes

= cos (x) - 1.23 + 1

Sumar/restar lo siguiente:

- 1.23 + 1 = - 0.23

= cos (x) - 0.23

= cos (x) - 0.23

- 0.23 + cos (x) = 0

Desplace

0.23

a la derecha

- 0.23 + cos (x) = 0

Sumar

0.23

a ambos lados

- 0.23 + cos (x) + 0.23 = 0 + 0.23

Simplificar

cos (x) = 0.23

cos (x) = 0.23

Aplicar propiedades trigonométricas inversas

cos (x) = 0.23

Soluciones generales para

cos (x) = 0.23

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

x = arccos (0.23) + 2 πn, x = 2 π - arccos (0.23) + 2 πn

x = arccos (0.23) + 2 πn, x = 2 π - arccos (0.23) + 2 πn

Mostrar soluciones en forma decimal

x = 1.33871 \dots + 2 πn, x = 2 π - 1.33871 \dots + 2 πn

Gráfica

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