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

Solución

resolver para

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

Solución

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

Mover

y

al lado derecho

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}

Ejemplos populares

csc(θ)= 3/2 , pi/2 <θ<(3pi)/2

csc (θ) = \frac{3}{2}, \frac{π}{2} < θ < \frac{3 π}{2}

tan(x)=(5.1)/(4.2)

tan (x) = \frac{5.1}{4.2}

tan(3x)*tan(30)=1

tan (3 x) \cdot tan (3 0^{\circ}) = 1

3 - 6 sin (2 x) = 0

1/1+cot^2(x)=sin^2(x)

\frac{1}{1} + cot^{2} (x) = sin^{2} (x)