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-ac_{1}sin(ax)+ac_{2}cos(ax)=0

Solución

- a c_{1} sin (a x) + a c_{2} cos (a x) = 0

Solución

x = \frac{arctan ( \frac{c _{2}}{c _{1}} )}{a} + \frac{πn}{a}

Pasos de solución

- a c_{1} sin (a x) + a c_{2} cos (a x) = 0

Re-escribir usando identidades trigonométricas

- a c_{1} sin (a x) + a c_{2} cos (a x) = 0

Dividir ambos lados entre

cos (a x), cos (a x) \neq = 0

\frac{- a c _{1} sin ( a x ) + a c _{2} cos ( a x )}{cos ( a x )} = \frac{0}{cos ( a x )}

Simplificar

- \frac{a c _{1} sin ( a x )}{cos ( a x )} + a c_{2} = 0

Utilizar la identidad trigonométrica básica:

\frac{sin ( x )}{cos ( x )} = tan (x)

- a c_{1} tan (a x) + a c_{2} = 0

- a c_{1} tan (a x) + a c_{2} = 0

Mover

a c_{2}

al lado derecho

- a c_{1} tan (a x) + a c_{2} = 0

Restar

a c_{2}

de ambos lados

- a c_{1} tan (a x) + a c_{2} - a c_{2} = 0 - a c_{2}

Simplificar

- a c_{1} tan (a x) = - a c_{2}

- a c_{1} tan (a x) = - a c_{2}

Dividir ambos lados entre

- a c_{1}; a \neq = 0

- a c_{1} tan (a x) = - a c_{2}

Dividir ambos lados entre

- a c_{1}; a \neq = 0

\frac{- a c _{1} tan ( a x )}{- a c _{1}} = \frac{- a c _{2}}{- a c _{1}}; a \neq = 0

Simplificar

\frac{- a c _{1} tan ( a x )}{- a c _{1}} = \frac{- a c _{2}}{- a c _{1}}

Simplificar

\frac{- a c _{1} tan ( a x )}{- a c _{1}} : tan (a x)

\frac{- a c _{1} tan ( a x )}{- a c _{1}}

Aplicar las propiedades de las fracciones:

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

= \frac{a c _{1} tan ( a x )}{a c _{1}}

Eliminar los terminos comunes:

a

= \frac{c _{1} tan ( a x )}{c _{1}}

Eliminar los terminos comunes:

c_{1}

= tan (a x)

Simplificar

\frac{- a c _{2}}{- a c _{1}} : \frac{c _{2}}{c _{1}}

\frac{- a c _{2}}{- a c _{1}}

Aplicar las propiedades de las fracciones:

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

= \frac{a c _{2}}{a c _{1}}

Eliminar los terminos comunes:

a

= \frac{c _{2}}{c _{1}}

tan (a x) = \frac{c _{2}}{c _{1}}; a \neq = 0

tan (a x) = \frac{c _{2}}{c _{1}}; a \neq = 0

tan (a x) = \frac{c _{2}}{c _{1}}; a \neq = 0

Aplicar propiedades trigonométricas inversas

tan (a x) = \frac{c _{2}}{c _{1}}

Soluciones generales para

tan (a x) = \frac{c _{2}}{c _{1}}

tan (x) = a \Rightarrow x = arctan (a) + πn

a x = arctan (\frac{c _{2}}{c _{1}}) + πn

a x = arctan (\frac{c _{2}}{c _{1}}) + πn

Resolver

a x = arctan (\frac{c _{2}}{c _{1}}) + πn : x = \frac{arctan ( \frac{c _{2}}{c _{1}} )}{a} + \frac{πn}{a}; a \neq = 0

a x = arctan (\frac{c _{2}}{c _{1}}) + πn

Dividir ambos lados entre

a; a \neq = 0

a x = arctan (\frac{c _{2}}{c _{1}}) + πn

Dividir ambos lados entre

a; a \neq = 0

\frac{a x}{a} = \frac{arctan ( \frac{c _{2}}{c _{1}} )}{a} + \frac{πn}{a}; a \neq = 0

Simplificar

x = \frac{arctan ( \frac{c _{2}}{c _{1}} )}{a} + \frac{πn}{a}; a \neq = 0

x = \frac{arctan ( \frac{c _{2}}{c _{1}} )}{a} + \frac{πn}{a}; a \neq = 0

x = \frac{arctan ( \frac{c _{2}}{c _{1}} )}{a} + \frac{πn}{a}

Ejemplos populares

3 - 3 cos (x) = 0

-2cot(x)=csc^2(x)

- 2 cot (x) = csc^{2} (x)

sin (θ) = - 0.671

cos (y) = sin (y)

(sin^2(x)+5cos^2(x))/2 =2

\frac{sin ^{2} ( x ) + 5 cos ^{2} ( x )}{2} = 2