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Popular >

solvefor θ,r=-3/(rcos(θ))

Solución

resolver para

θ, r = - \frac{3}{r cos ( θ )}

Solución

θ = arccos (- \frac{3}{r ^{2}}) + 2 πn, θ = - arccos (- \frac{3}{r ^{2}}) + 2 πn

Pasos de solución

r = - \frac{3}{r cos ( θ )}

Intercambiar lados

- \frac{3}{r cos ( θ )} = r

Multiplicar ambos lados por

cos (θ)

- \frac{3}{r cos ( θ )} = r

Multiplicar ambos lados por

cos (θ)

- \frac{3}{r cos ( θ )} cos (θ) = r cos (θ)

Simplificar

- \frac{3}{r} = r cos (θ)

- \frac{3}{r} = r cos (θ)

Intercambiar lados

r cos (θ) = - \frac{3}{r}

Dividir ambos lados entre

r; r \neq = 0

r cos (θ) = - \frac{3}{r}

Dividir ambos lados entre

r; r \neq = 0

\frac{r cos ( θ )}{r} = \frac{- \frac{3}{r}}{r}; r \neq = 0

Simplificar

\frac{r cos ( θ )}{r} = \frac{- \frac{3}{r}}{r}

Simplificar

\frac{r cos ( θ )}{r} : cos (θ)

\frac{r cos ( θ )}{r}

Eliminar los terminos comunes:

r

= cos (θ)

Simplificar

\frac{- \frac{3}{r}}{r} : - \frac{3}{r ^{2}}

\frac{- \frac{3}{r}}{r}

Aplicar las propiedades de las fracciones:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{\frac{3}{r}}{r}

Aplicar las propiedades de las fracciones:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

\frac{\frac{3}{r}}{r} = \frac{3}{rr}

= - \frac{3}{rr}

rr = r^{2}

rr

Aplicar las leyes de los exponentes:

a^{b} \cdot a^{c} = a^{b + c}

rr = r^{1 + 1}

= r^{1 + 1}

Sumar:

1 + 1 = 2

= r^{2}

= - \frac{3}{r ^{2}}

cos (θ) = - \frac{3}{r ^{2}}; r \neq = 0

cos (θ) = - \frac{3}{r ^{2}}; r \neq = 0

cos (θ) = - \frac{3}{r ^{2}}; r \neq = 0

Aplicar propiedades trigonométricas inversas

cos (θ) = - \frac{3}{r ^{2}}

Soluciones generales para

cos (θ) = - \frac{3}{r ^{2}}

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

θ = arccos (- \frac{3}{r ^{2}}) + 2 πn, θ = - arccos (- \frac{3}{r ^{2}}) + 2 πn

θ = arccos (- \frac{3}{r ^{2}}) + 2 πn, θ = - arccos (- \frac{3}{r ^{2}}) + 2 πn

Ejemplos populares

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

sin^{2} (x) + sin (2 x) = 1

solvefor T,y=sin(2T)resolver para

T, y = sin (2 T)

sin (4 7^{\circ}) = cos (x)

0.82=0.102cos(3.715t)

0.82 = 0.102 cos (3.715 t)

sin^2(x)+0.49=1

sin^{2} (x) + 0.49 = 1