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Popular >

7cos(2x)=7sin^2(x)+5

Solución

7 cos (2 x) = 7 sin^{2} (x) + 5

Solución

x = 0.31372 \dots + 2 πn, x = π - 0.31372 \dots + 2 πn, x = - 0.31372 \dots + 2 πn, x = π + 0.31372 \dots + 2 πn

Grados

x = 17.97528 \dots^{\circ} + 36 0^{\circ} n, x = 162.02471 \dots^{\circ} + 36 0^{\circ} n, x = - 17.97528 \dots^{\circ} + 36 0^{\circ} n, x = 197.97528 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

7 cos (2 x) = 7 sin^{2} (x) + 5

Restar

7 sin^{2} (x) + 5

de ambos lados

7 cos (2 x) - 7 sin^{2} (x) - 5 = 0

Re-escribir usando identidades trigonométricas

- 5 + 7 cos (2 x) - 7 sin^{2} (x)

Utilizar la identidad trigonométrica del ángulo doble:

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

= - 5 + 7 (1 - 2 sin^{2} (x)) - 7 sin^{2} (x)

Simplificar

- 5 + 7 (1 - 2 sin^{2} (x)) - 7 sin^{2} (x) : - 21 sin^{2} (x) + 2

- 5 + 7 (1 - 2 sin^{2} (x)) - 7 sin^{2} (x)

Expandir

7 (1 - 2 sin^{2} (x)) : 7 - 14 sin^{2} (x)

7 (1 - 2 sin^{2} (x))

Poner los parentesis utilizando:

a (b - c) = ab - a c

a = 7, b = 1, c = 2 sin^{2} (x)

= 7 \cdot 1 - 7 \cdot 2 sin^{2} (x)

Simplificar

7 \cdot 1 - 7 \cdot 2 sin^{2} (x) : 7 - 14 sin^{2} (x)

7 \cdot 1 - 7 \cdot 2 sin^{2} (x)

Multiplicar los numeros:

7 \cdot 1 = 7

= 7 - 7 \cdot 2 sin^{2} (x)

Multiplicar los numeros:

7 \cdot 2 = 14

= 7 - 14 sin^{2} (x)

= 7 - 14 sin^{2} (x)

= - 5 + 7 - 14 sin^{2} (x) - 7 sin^{2} (x)

Simplificar

- 5 + 7 - 14 sin^{2} (x) - 7 sin^{2} (x) : - 21 sin^{2} (x) + 2

- 5 + 7 - 14 sin^{2} (x) - 7 sin^{2} (x)

Sumar elementos similares:

- 14 sin^{2} (x) - 7 sin^{2} (x) = - 21 sin^{2} (x)

= - 5 + 7 - 21 sin^{2} (x)

Sumar/restar lo siguiente:

- 5 + 7 = 2

= - 21 sin^{2} (x) + 2

= - 21 sin^{2} (x) + 2

= - 21 sin^{2} (x) + 2

2 - 21 sin^{2} (x) = 0

Usando el método de sustitución

2 - 21 sin^{2} (x) = 0

Sea:

sin (x) = u

2 - 21 u^{2} = 0

2 - 21 u^{2} = 0 : u = \frac{2}{21}, u = - \frac{2}{21}

2 - 21 u^{2} = 0

Mover

2

al lado derecho

2 - 21 u^{2} = 0

Restar

2

de ambos lados

2 - 21 u^{2} - 2 = 0 - 2

Simplificar

- 21 u^{2} = - 2

- 21 u^{2} = - 2

Dividir ambos lados entre

- 21

- 21 u^{2} = - 2

Dividir ambos lados entre

- 21

\frac{- 21 u ^{2}}{- 21} = \frac{- 2}{- 21}

Simplificar

u^{2} = \frac{2}{21}

u^{2} = \frac{2}{21}

Para

x^{2} = f (a)

las soluciones son

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

u = \frac{2}{21}, u = - \frac{2}{21}

Sustituir en la ecuación

u = sin (x)

sin (x) = \frac{2}{21}, sin (x) = - \frac{2}{21}

sin (x) = \frac{2}{21}, sin (x) = - \frac{2}{21}

sin (x) = \frac{2}{21} : x = arcsin (\frac{2}{21}) + 2 πn, x = π - arcsin (\frac{2}{21}) + 2 πn

sin (x) = \frac{2}{21}

Aplicar propiedades trigonométricas inversas

sin (x) = \frac{2}{21}

Soluciones generales para

sin (x) = \frac{2}{21}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (\frac{2}{21}) + 2 πn, x = π - arcsin (\frac{2}{21}) + 2 πn

x = arcsin (\frac{2}{21}) + 2 πn, x = π - arcsin (\frac{2}{21}) + 2 πn

sin (x) = - \frac{2}{21} : x = arcsin (- \frac{2}{21}) + 2 πn, x = π + arcsin (\frac{2}{21}) + 2 πn

sin (x) = - \frac{2}{21}

Aplicar propiedades trigonométricas inversas

sin (x) = - \frac{2}{21}

Soluciones generales para

sin (x) = - \frac{2}{21}

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (- \frac{2}{21}) + 2 πn, x = π + arcsin (\frac{2}{21}) + 2 πn

x = arcsin (- \frac{2}{21}) + 2 πn, x = π + arcsin (\frac{2}{21}) + 2 πn

Combinar toda las soluciones

x = arcsin (\frac{2}{21}) + 2 πn, x = π - arcsin (\frac{2}{21}) + 2 πn, x = arcsin (- \frac{2}{21}) + 2 πn, x = π + arcsin (\frac{2}{21}) + 2 πn

Mostrar soluciones en forma decimal

x = 0.31372 \dots + 2 πn, x = π - 0.31372 \dots + 2 πn, x = - 0.31372 \dots + 2 πn, x = π + 0.31372 \dots + 2 πn

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

(cos(x)*cot(x))/(1-sin(x))=3

\frac{cos ( x ) \cdot cot ( x )}{1 - sin ( x )} = 3

(sin(8))/(30)=(sin(θ))/(120)

\frac{sin ( 8 )}{30} = \frac{sin ( θ )}{120}

114=sin(x)

114 = sin (x)

cos(θ)=(11.14)/(13)

cos (θ) = \frac{11.14}{13}