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solvefor θ,r=vcos(θ)((2vsin(θ))/g)

Solución

resolver para

θ, r = v cos (θ) (\frac{2 v sin ( θ )}{g})

Solución

θ = \frac{arcsin ( \frac{g r}{v ^{2}} )}{2} + πn, θ = \frac{π}{2} + \frac{arcsin ( - \frac{g r}{v ^{2}} )}{2} + πn

Pasos de solución

r = v cos (θ) (\frac{2 v sin ( θ )}{g})

Intercambiar lados

v cos (θ) \frac{2 v sin ( θ )}{g} = r

Restar

r

de ambos lados

\frac{2 v ^{2} sin ( θ ) cos ( θ )}{g} - r = 0

Simplificar

\frac{2 v ^{2} sin ( θ ) cos ( θ )}{g} - r : \frac{2 v ^{2} sin ( θ ) cos ( θ ) - g r}{g}

\frac{2 v ^{2} sin ( θ ) cos ( θ )}{g} - r

Convertir a fracción:

r = \frac{r g}{g}

= \frac{2 v ^{2} sin ( θ ) cos ( θ )}{g} - \frac{r g}{g}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{2 v ^{2} sin ( θ ) cos ( θ ) - r g}{g}

\frac{2 v ^{2} sin ( θ ) cos ( θ ) - g r}{g} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

2 v^{2} sin (θ) cos (θ) - g r = 0

Re-escribir usando identidades trigonométricas

2 v^{2} sin (θ) cos (θ) - g r

Utilizar la identidad trigonométrica del ángulo doble:

2 sin (x) cos (x) = sin (2 x)

= - g r + sin (2 θ) v^{2}

- g r + sin (2 θ) v^{2} = 0

Mover

g r

al lado derecho

- g r + sin (2 θ) v^{2} = 0

Sumar

g r

a ambos lados

- g r + sin (2 θ) v^{2} + g r = 0 + g r

Simplificar

sin (2 θ) v^{2} = g r

sin (2 θ) v^{2} = g r

Dividir ambos lados entre

v^{2}; v \neq = 0

sin (2 θ) v^{2} = g r

Dividir ambos lados entre

v^{2}; v \neq = 0

\frac{sin ( 2 θ ) v ^{2}}{v ^{2}} = \frac{g r}{v ^{2}}; v \neq = 0

Simplificar

sin (2 θ) = \frac{g r}{v ^{2}}; v \neq = 0

sin (2 θ) = \frac{g r}{v ^{2}}; v \neq = 0

Aplicar propiedades trigonométricas inversas

sin (2 θ) = \frac{g r}{v ^{2}}

Soluciones generales para

sin (2 θ) = \frac{g r}{v ^{2}}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π + arcsin (a) + 2 πn

2 θ = arcsin (\frac{g r}{v ^{2}}) + 2 πn, 2 θ = π + arcsin (- \frac{g r}{v ^{2}}) + 2 πn

2 θ = arcsin (\frac{g r}{v ^{2}}) + 2 πn, 2 θ = π + arcsin (- \frac{g r}{v ^{2}}) + 2 πn

Resolver

2 θ = arcsin (\frac{g r}{v ^{2}}) + 2 πn : θ = \frac{arcsin ( \frac{g r}{v ^{2}} )}{2} + πn

2 θ = arcsin (\frac{g r}{v ^{2}}) + 2 πn

Dividir ambos lados entre

2

2 θ = arcsin (\frac{g r}{v ^{2}}) + 2 πn

Dividir ambos lados entre

2

\frac{2 θ}{2} = \frac{arcsin ( \frac{g r}{v ^{2}} )}{2} + \frac{2 πn}{2}

Simplificar

θ = \frac{arcsin ( \frac{g r}{v ^{2}} )}{2} + πn

θ = \frac{arcsin ( \frac{g r}{v ^{2}} )}{2} + πn

Resolver

2 θ = π + arcsin (- \frac{g r}{v ^{2}}) + 2 πn : θ = \frac{π}{2} + \frac{arcsin ( - \frac{g r}{v ^{2}} )}{2} + πn

2 θ = π + arcsin (- \frac{g r}{v ^{2}}) + 2 πn

Dividir ambos lados entre

2

2 θ = π + arcsin (- \frac{g r}{v ^{2}}) + 2 πn

Dividir ambos lados entre

2

\frac{2 θ}{2} = \frac{π}{2} + \frac{arcsin ( - \frac{g r}{v ^{2}} )}{2} + \frac{2 πn}{2}

Simplificar

θ = \frac{π}{2} + \frac{arcsin ( - \frac{g r}{v ^{2}} )}{2} + πn

θ = \frac{π}{2} + \frac{arcsin ( - \frac{g r}{v ^{2}} )}{2} + πn

θ = \frac{arcsin ( \frac{g r}{v ^{2}} )}{2} + πn, θ = \frac{π}{2} + \frac{arcsin ( - \frac{g r}{v ^{2}} )}{2} + πn

Ejemplos populares

5=5+4cos(θ)

5 = 5 + 4 cos (θ)

cos(θ)=-0.47

cos (θ) = - 0.47

1+tan^2(x)cos(x)=sec(x)

1 + tan^{2} (x) cos (x) = sec (x)

sec(θ)=(sqrt(6))/2

sec (θ) = \frac{6}{2}

sin^2(x)+cos^2(x)=sin(x)csc^2(x)

sin^{2} (x) + cos^{2} (x) = sin (x) csc^{2} (x)