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Popular Trigonometría >

solvefor x,(sin(pix)+cos(piy))^5=36

Solución

resolver para

x, (sin (π x) + cos (π y))^{5} = 36

Solución

x = \frac{arcsin ( 5 36 - cos ( π y ) )}{π} + 2 n, x = 1 + \frac{arcsin ( - 5 36 + cos ( π y ) )}{π} + 2 n

Pasos de solución

(sin (π x) + cos (π y))^{5} = 36

Para

(g (x))^{n} = f (a)

, n es impar, la solución es

g (x) = n f (a)

Resolver

sin (π x) + cos (π y) = 536 : sin (π x) = 536 - cos (π y)

sin (π x) + cos (π y) = 536

Desplace

cos (π y)

a la derecha

sin (π x) + cos (π y) = 536

Restar

cos (π y)

de ambos lados

sin (π x) + cos (π y) - cos (π y) = 536 - cos (π y)

Simplificar

sin (π x) = 536 - cos (π y)

sin (π x) = 536 - cos (π y)

La solución es

sin (π x) = 536 - cos (π y)

Aplicar propiedades trigonométricas inversas

sin (π x) = 536 - cos (π y)

Soluciones generales para

sin (π x) = 536 - cos (π y)

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

π x = arcsin (536 - cos (π y)) + 2 πn, π x = π + arcsin (- 536 + cos (π y)) + 2 πn

π x = arcsin (536 - cos (π y)) + 2 πn, π x = π + arcsin (- 536 + cos (π y)) + 2 πn

Resolver

π x = arcsin (536 - cos (π y)) + 2 πn : x = \frac{arcsin ( 5 36 - cos ( π y ) )}{π} + 2 n

π x = arcsin (536 - cos (π y)) + 2 πn

Dividir ambos lados entre

π

π x = arcsin (536 - cos (π y)) + 2 πn

Dividir ambos lados entre

π

\frac{π x}{π} = \frac{arcsin ( 5 36 - cos ( π y ) )}{π} + \frac{2 πn}{π}

Simplificar

x = \frac{arcsin ( 5 36 - cos ( π y ) )}{π} + 2 n

x = \frac{arcsin ( 5 36 - cos ( π y ) )}{π} + 2 n

Resolver

π x = π + arcsin (- 536 + cos (π y)) + 2 πn : x = 1 + \frac{arcsin ( - 5 36 + cos ( π y ) )}{π} + 2 n

π x = π + arcsin (- 536 + cos (π y)) + 2 πn

Dividir ambos lados entre

π

π x = π + arcsin (- 536 + cos (π y)) + 2 πn

Dividir ambos lados entre

π

\frac{π x}{π} = \frac{π}{π} + \frac{arcsin ( - 5 36 + cos ( π y ) )}{π} + \frac{2 πn}{π}

Simplificar

\frac{π x}{π} = \frac{π}{π} + \frac{arcsin ( - 5 36 + cos ( π y ) )}{π} + \frac{2 πn}{π}

Simplificar

\frac{π x}{π} : x

\frac{π x}{π}

Eliminar los terminos comunes:

π

= x

Simplificar

\frac{π}{π} + \frac{arcsin ( - 5 36 + cos ( π y ) )}{π} + \frac{2 πn}{π} : 1 + \frac{arcsin ( - 5 36 + cos ( π y ) )}{π} + 2 n

\frac{π}{π} + \frac{arcsin ( - 5 36 + cos ( π y ) )}{π} + \frac{2 πn}{π}

Aplicar la regla

\frac{a}{a} = 1

\frac{π}{π} = 1

= 1 + \frac{arcsin ( cos ( π y ) - 5 36 )}{π} + \frac{2 πn}{π}

Cancelar

\frac{2 πn}{π} : 2 n

\frac{2 πn}{π}

Eliminar los terminos comunes:

π

= 2 n

= 1 + \frac{arcsin ( cos ( π y ) - 5 36 )}{π} + 2 n

x = 1 + \frac{arcsin ( - 5 36 + cos ( π y ) )}{π} + 2 n

x = 1 + \frac{arcsin ( - 5 36 + cos ( π y ) )}{π} + 2 n

x = 1 + \frac{arcsin ( - 5 36 + cos ( π y ) )}{π} + 2 n

x = \frac{arcsin ( 5 36 - cos ( π y ) )}{π} + 2 n, x = 1 + \frac{arcsin ( - 5 36 + cos ( π y ) )}{π} + 2 n

Gráfica

Ejemplos populares

sin(θ)=-(sqrt(2))/2 ,0<= θ<2pi

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2sin(1/2 x)+sqrt(2)=0

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(cos(x))/(sin(x))=-0.05467

\frac{cos ( x )}{sin ( x )} = - 0.05467

(1+4cos(θ))^2=(sqrt(3)sin(θ))^2

(1 + 4 cos (θ))^{2} = (3 sin (θ))^{2}

1/(tan(x))=4

\frac{1}{tan ( x )} = 4