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solvefor θ,r= 7/(1+cos(θ))

Solución

resolver para

θ, r = \frac{7}{1 + cos ( θ )}

Solución

θ = arccos (\frac{7}{r} - 1) + 2 πn, θ = - arccos (\frac{7}{r} - 1) + 2 πn

Pasos de solución

r = \frac{7}{1 + cos ( θ )}

Intercambiar lados

\frac{7}{1 + cos ( θ )} = r

Multiplicar ambos lados por

1 + cos (θ)

\frac{7}{1 + cos ( θ )} = r

Multiplicar ambos lados por

1 + cos (θ)

\frac{7}{1 + cos ( θ )} (1 + cos (θ)) = r (1 + cos (θ))

Simplificar

7 = r (1 + cos (θ))

7 = r (1 + cos (θ))

Intercambiar lados

r (1 + cos (θ)) = 7

Dividir ambos lados entre

r; r \neq = 0

r (1 + cos (θ)) = 7

Dividir ambos lados entre

r; r \neq = 0

\frac{r ( 1 + cos ( θ ) )}{r} = \frac{7}{r}; r \neq = 0

Simplificar

1 + cos (θ) = \frac{7}{r}; r \neq = 0

1 + cos (θ) = \frac{7}{r}; r \neq = 0

Mover

1

al lado derecho

1 + cos (θ) = \frac{7}{r}; r \neq = 0

Restar

1

de ambos lados

1 + cos (θ) - 1 = \frac{7}{r} - 1; r \neq = 0

Simplificar

cos (θ) = \frac{7}{r} - 1; r \neq = 0

cos (θ) = \frac{7}{r} - 1; r \neq = 0

Aplicar propiedades trigonométricas inversas

cos (θ) = \frac{7}{r} - 1

Soluciones generales para

cos (θ) = \frac{7}{r} - 1

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

θ = arccos (\frac{7}{r} - 1) + 2 πn, θ = - arccos (\frac{7}{r} - 1) + 2 πn

θ = arccos (\frac{7}{r} - 1) + 2 πn, θ = - arccos (\frac{7}{r} - 1) + 2 πn

Ejemplos populares

csc(θ)=-3/(sqrt(5)),tan(2θ)

csc (θ) = - \frac{3}{5}, tan (2 θ)

sqrt(1-sin(x))=0

1 - sin (x) = 0

solvefor x,sin(x)=e resolver para

x, sin (x) = e

solvefor x,sin(x)=3 resolver para

x, sin (x) = 3

3cos(2θ)+5cos(θ)+2=0

3 cos (2 θ) + 5 cos (θ) + 2 = 0