cos(x+2*pi/3)=-12 la ecuación
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Solución
Solución detallada
Tenemos la ecuación
$$\cos{\left(x + \frac{2 \pi}{3} \right)} = -12$$
es la ecuación trigonométrica más simple
Dividamos ambos miembros de la ecuación en -1
La ecuación se convierte en
$$\sin{\left(x + \frac{\pi}{6} \right)} = 12$$
Como el miembro derecho de la ecuación
en el módulo =
True
pero sin
no puede ser más de 1 o menos de -1
significa que la ecuación correspondiente no tiene solución.
pi
x1 = - -- + I*im(asin(12)) + re(asin(12))
6
$$x_{1} = - \frac{\pi}{6} + \operatorname{re}{\left(\operatorname{asin}{\left(12 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(12 \right)}\right)}$$
5*pi
x2 = -re(asin(12)) + ---- - I*im(asin(12))
6
$$x_{2} = - \operatorname{re}{\left(\operatorname{asin}{\left(12 \right)}\right)} + \frac{5 \pi}{6} - i \operatorname{im}{\left(\operatorname{asin}{\left(12 \right)}\right)}$$
x2 = -re(asin(12)) + 5*pi/6 - i*im(asin(12))
Suma y producto de raíces
[src]
pi 5*pi
- -- + I*im(asin(12)) + re(asin(12)) + -re(asin(12)) + ---- - I*im(asin(12))
6 6
$$\left(- \frac{\pi}{6} + \operatorname{re}{\left(\operatorname{asin}{\left(12 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(12 \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(12 \right)}\right)} + \frac{5 \pi}{6} - i \operatorname{im}{\left(\operatorname{asin}{\left(12 \right)}\right)}\right)$$
$$\frac{2 \pi}{3}$$
/ pi \ / 5*pi \
|- -- + I*im(asin(12)) + re(asin(12))|*|-re(asin(12)) + ---- - I*im(asin(12))|
\ 6 / \ 6 /
$$\left(- \frac{\pi}{6} + \operatorname{re}{\left(\operatorname{asin}{\left(12 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(12 \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{asin}{\left(12 \right)}\right)} + \frac{5 \pi}{6} - i \operatorname{im}{\left(\operatorname{asin}{\left(12 \right)}\right)}\right)$$
-(-pi + 6*re(asin(12)) + 6*I*im(asin(12)))*(-5*pi + 6*re(asin(12)) + 6*I*im(asin(12)))
---------------------------------------------------------------------------------------
36
$$- \frac{\left(- 5 \pi + 6 \operatorname{re}{\left(\operatorname{asin}{\left(12 \right)}\right)} + 6 i \operatorname{im}{\left(\operatorname{asin}{\left(12 \right)}\right)}\right) \left(- \pi + 6 \operatorname{re}{\left(\operatorname{asin}{\left(12 \right)}\right)} + 6 i \operatorname{im}{\left(\operatorname{asin}{\left(12 \right)}\right)}\right)}{36}$$
-(-pi + 6*re(asin(12)) + 6*i*im(asin(12)))*(-5*pi + 6*re(asin(12)) + 6*i*im(asin(12)))/36
x1 = 1.0471975511966 - 3.17631318059166*i
x2 = 1.0471975511966 + 3.17631318059166*i
x2 = 1.0471975511966 + 3.17631318059166*i