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solvefor x,(d^2x)/(dt^2)+10sin(x)=5

Solución

resolver para

x, \frac{d ^{2} x}{d t ^{2}} + 10 sin (x) = 5

Solución

x = arcsin (\frac{5 - \frac{d ^{2} x}{d t ^{2}}}{10}) + 2 πn, x = π + arcsin (- \frac{5 - \frac{d ^{2} x}{d t ^{2}}}{10}) + 2 πn

Pasos de solución

\frac{d ^{2} x}{d t ^{2}} + 10 sin (x) = 5

Desplace

\frac{d ^{2} x}{d t ^{2}}

a la derecha

\frac{d ^{2} x}{d t ^{2}} + 10 sin (x) = 5

Restar

\frac{d ^{2} x}{d t ^{2}}

de ambos lados

\frac{d ^{2} x}{d t ^{2}} + 10 sin (x) - \frac{d ^{2} x}{d t ^{2}} = 5 - \frac{d ^{2} x}{d t ^{2}}

Simplificar

10 sin (x) = 5 - \frac{d ^{2} x}{d t ^{2}}

10 sin (x) = 5 - \frac{d ^{2} x}{d t ^{2}}

Dividir ambos lados entre

10

10 sin (x) = 5 - \frac{d ^{2} x}{d t ^{2}}

Dividir ambos lados entre

10

\frac{10 sin ( x )}{10} = \frac{5}{10} - \frac{\frac{d ^{2} x}{d t ^{2}}}{10}

Simplificar

\frac{10 sin ( x )}{10} = \frac{5}{10} - \frac{\frac{d ^{2} x}{d t ^{2}}}{10}

Simplificar

\frac{10 sin ( x )}{10} : sin (x)

\frac{10 sin ( x )}{10}

Dividir:

\frac{10}{10} = 1

= sin (x)

Simplificar

\frac{5}{10} - \frac{\frac{d ^{2} x}{d t ^{2}}}{10} : \frac{5 - \frac{d ^{2} x}{d t ^{2}}}{10}

\frac{5}{10} - \frac{\frac{d ^{2} x}{d t ^{2}}}{10}

Aplicar la regla

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{5 - \frac{d ^{2} x}{d t ^{2}}}{10}

sin (x) = \frac{5 - \frac{d ^{2} x}{d t ^{2}}}{10}

sin (x) = \frac{5 - \frac{d ^{2} x}{d t ^{2}}}{10}

sin (x) = \frac{5 - \frac{d ^{2} x}{d t ^{2}}}{10}

Aplicar propiedades trigonométricas inversas

sin (x) = \frac{5 - \frac{d ^{2} x}{d t ^{2}}}{10}

Soluciones generales para

sin (x) = \frac{5 - \frac{d ^{2} x}{d t ^{2}}}{10}

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

x = arcsin (\frac{5 - \frac{d ^{2} x}{d t ^{2}}}{10}) + 2 πn, x = π + arcsin (- \frac{5 - \frac{d ^{2} x}{d t ^{2}}}{10}) + 2 πn

x = arcsin (\frac{5 - \frac{d ^{2} x}{d t ^{2}}}{10}) + 2 πn, x = π + arcsin (- \frac{5 - \frac{d ^{2} x}{d t ^{2}}}{10}) + 2 πn

Gráfica

Ejemplos populares

2 - 6 cos (x) = 0

sec^2(x)tan^2(x)=sin^2(x)

sec^{2} (x) tan^{2} (x) = sin^{2} (x)

12 sin^{2} (θ) = 3

4sin^2(θ)+2cos^2(θ)=3

4 sin^{2} (θ) + 2 cos^{2} (θ) = 3

ω=360lb*5sec(x)

ω = 360 l b \cdot 5 sec (x)