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solvefor x,y=5cos(8x)-y

Solución

solvefor

x = \frac{arccos ( \frac{2 y}{5} )}{8} + \frac{πn}{4}, x = - \frac{arccos ( \frac{2 y}{5} )}{8} + \frac{πn}{4}

Pasos de solución

y = 5 cos (8 x) - y

Intercambiar lados

5 cos (8 x) - y = y

Desplace

y

a la derecha

5 cos (8 x) - y = y

Sumar

y

a ambos lados

5 cos (8 x) - y + y = y + y

Simplificar

5 cos (8 x) = 2 y

5 cos (8 x) = 2 y

Dividir ambos lados entre

5

5 cos (8 x) = 2 y

Dividir ambos lados entre

5

\frac{5 cos ( 8 x )}{5} = \frac{2 y}{5}

Simplificar

cos (8 x) = \frac{2 y}{5}

cos (8 x) = \frac{2 y}{5}

Aplicar propiedades trigonométricas inversas

cos (8 x) = \frac{2 y}{5}

Soluciones generales para

cos (8 x) = \frac{2 y}{5}

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

8 x = arccos (\frac{2 y}{5}) + 2 πn, 8 x = - arccos (\frac{2 y}{5}) + 2 πn

8 x = arccos (\frac{2 y}{5}) + 2 πn, 8 x = - arccos (\frac{2 y}{5}) + 2 πn

Resolver

8 x = arccos (\frac{2 y}{5}) + 2 πn : x = \frac{arccos ( \frac{2 y}{5} )}{8} + \frac{πn}{4}

8 x = arccos (\frac{2 y}{5}) + 2 πn

Dividir ambos lados entre

8

8 x = arccos (\frac{2 y}{5}) + 2 πn

Dividir ambos lados entre

8

\frac{8 x}{8} = \frac{arccos ( \frac{2 y}{5} )}{8} + \frac{2 πn}{8}

Simplificar

x = \frac{arccos ( \frac{2 y}{5} )}{8} + \frac{πn}{4}

x = \frac{arccos ( \frac{2 y}{5} )}{8} + \frac{πn}{4}

Resolver

8 x = - arccos (\frac{2 y}{5}) + 2 πn : x = - \frac{arccos ( \frac{2 y}{5} )}{8} + \frac{πn}{4}

8 x = - arccos (\frac{2 y}{5}) + 2 πn

Dividir ambos lados entre

8

8 x = - arccos (\frac{2 y}{5}) + 2 πn

Dividir ambos lados entre

8

\frac{8 x}{8} = - \frac{arccos ( \frac{2 y}{5} )}{8} + \frac{2 πn}{8}

Simplificar

x = - \frac{arccos ( \frac{2 y}{5} )}{8} + \frac{πn}{4}

x = - \frac{arccos ( \frac{2 y}{5} )}{8} + \frac{πn}{4}

x = \frac{arccos ( \frac{2 y}{5} )}{8} + \frac{πn}{4}, x = - \frac{arccos ( \frac{2 y}{5} )}{8} + \frac{πn}{4}