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Popular >

r=(2a)/((1+cos(x)))

Solución

r = \frac{2 a}{( 1 + cos ( x ) )}

Solución

x = arccos (\frac{2 a}{r} - 1) + 2 πn, x = - arccos (\frac{2 a}{r} - 1) + 2 πn

Pasos de solución

r = \frac{2 a}{( 1 + cos ( x ) )}

Intercambiar lados

\frac{2 a}{1 + cos ( x )} = r

Multiplicar ambos lados por

1 + cos (x)

\frac{2 a}{1 + cos ( x )} = r

Multiplicar ambos lados por

1 + cos (x)

\frac{2 a}{1 + cos ( x )} (1 + cos (x)) = r (1 + cos (x))

Simplificar

2 a = r (1 + cos (x))

2 a = r (1 + cos (x))

Intercambiar lados

r (1 + cos (x)) = 2 a

Dividir ambos lados entre

r; r \neq = 0

r (1 + cos (x)) = 2 a

Dividir ambos lados entre

r; r \neq = 0

\frac{r ( 1 + cos ( x ) )}{r} = \frac{2 a}{r}; r \neq = 0

Simplificar

1 + cos (x) = \frac{2 a}{r}; r \neq = 0

1 + cos (x) = \frac{2 a}{r}; r \neq = 0

Mover

1

al lado derecho

1 + cos (x) = \frac{2 a}{r}; r \neq = 0

Restar

1

de ambos lados

1 + cos (x) - 1 = \frac{2 a}{r} - 1; r \neq = 0

Simplificar

cos (x) = \frac{2 a}{r} - 1; r \neq = 0

cos (x) = \frac{2 a}{r} - 1; r \neq = 0

Aplicar propiedades trigonométricas inversas

cos (x) = \frac{2 a}{r} - 1

Soluciones generales para

cos (x) = \frac{2 a}{r} - 1

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

x = arccos (\frac{2 a}{r} - 1) + 2 πn, x = - arccos (\frac{2 a}{r} - 1) + 2 πn

x = arccos (\frac{2 a}{r} - 1) + 2 πn, x = - arccos (\frac{2 a}{r} - 1) + 2 πn

Ejemplos populares

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cos^{3} (x) + cos^{2} (x) + cos (x) + 1 = 0

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\frac{cos ^{4} ( x )}{3} = sin^{2} (x)

sin^3(x)cos(x)-sin^2(x)=0

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cos^2(45-a)-sin^2(45-a)=sin^2(a)

cos^{2} (4 5^{\circ} - a) - sin^{2} (4 5^{\circ} - a) = sin^{2} (a)