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-a^2c_{1}cos(ax)-a^2c_{2}sin(ax)=0

Solución

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

Solución

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

Pasos de solución

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

Re-escribir usando identidades trigonométricas

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

Dividir ambos lados entre

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

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

Simplificar

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

Utilizar la identidad trigonométrica básica:

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

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

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

Mover

a^{2} c_{1}

al lado derecho

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

Sumar

a^{2} c_{1}

a ambos lados

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

Simplificar

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

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

Dividir ambos lados entre

- a^{2} c_{2}; a \neq = 0

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

Dividir ambos lados entre

- a^{2} c_{2}; a \neq = 0

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

Simplificar

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

Simplificar

\frac{- a ^{2} c _{2} tan ( a x )}{- a ^{2} c _{2}} : tan (a x)

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

Aplicar las propiedades de las fracciones:

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

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

Eliminar los terminos comunes:

a^{2}

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

Eliminar los terminos comunes:

c_{2}

= tan (a x)

Simplificar

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

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

Aplicar las propiedades de las fracciones:

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

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

Eliminar los terminos comunes:

a^{2}

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

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

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

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

Aplicar propiedades trigonométricas inversas

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

Soluciones generales para

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

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

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

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

Resolver

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

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

Dividir ambos lados entre

a; a \neq = 0

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

Dividir ambos lados entre

a; a \neq = 0

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

Simplificar

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

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

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

Ejemplos populares

10=-12sin(x)+1.8cos(x)

10 = - 12 sin (x) + 1.8 cos (x)

8tan(B)+12=3tan(B)+7

8 tan (B) + 12 = 3 tan (B) + 7

-2+sin(2θ)=-3/2

- 2 + sin (2 θ) = - \frac{3}{2}

tan (c) = \frac{24}{7}

sin (t) = \frac{- 1}{2}