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- La ecuación:
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Ecuación x=(x+1)/2
- Ecuación (x-6)(-5x-9)=0
-
Ecuación x^2-14*x+33=0
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Ecuación x^2+6=5x
- Expresar {x} en función de y en la ecuación:
- -13*x-19*y=17
- -9*x-12*y=-19
- -17*x-12*y=-9
- -8*x+3*y=-4
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Expresiones idénticas
- cos(x+a)=-sina
- coseno de (x más a) es igual a menos seno de a
- cosx+a=-sina
-
Expresiones semejantes
- cos(x-a)=-sina
- cos(x)*(cos(x)+a)^2=1
- cos2x+5cosx+a=0
- sin(a-b)-sin(a-b)=2*cos(a)*sin(b)
- cos(x+a)=+sina
- (-sin(a)-cos(a))/(2*cos(a)*cos((pi/2)-a)+1)=0
- (cosa-cosb)^2-(sina-sinb)^2
- -sin(a)+cos(pi/(a+2))=0
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Expresiones con funciones
- Coseno cos
- cos(x)^(2)=cos(x)
- cos2x+2(sqrt2)sin((pi/2)+x)-2=0
- cos(0,895+0,45)-1,2=x
- cos(x)-cos3x=sin(x)
- cos(5*x)^2=4
cos(x+a)=-sina la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos la ecuación
$$\cos{\left(a + x \right)} = - \sin{\left(a \right)}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$a + x = 2 \pi n + \operatorname{asin}{\left(- \sin{\left(a \right)} \right)}$$
$$a + x = 2 \pi n - \operatorname{asin}{\left(- \sin{\left(a \right)} \right)} + \pi$$
O
$$a + x = 2 \pi n - \operatorname{asin}{\left(\sin{\left(a \right)} \right)}$$
$$a + x = 2 \pi n + \operatorname{asin}{\left(\sin{\left(a \right)} \right)} + \pi$$
, donde n es cualquier número entero
Transportemos
$$a$$
al miembro derecho de la ecuación
con el signo opuesto, en total:
$$x = - a + 2 \pi n - \operatorname{asin}{\left(\sin{\left(a \right)} \right)}$$
$$x = - a + 2 \pi n + \operatorname{asin}{\left(\sin{\left(a \right)} \right)} + \pi$$
$$\cos{\left(a + x \right)} = - \sin{\left(a \right)}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$a + x = 2 \pi n + \operatorname{asin}{\left(- \sin{\left(a \right)} \right)}$$
$$a + x = 2 \pi n - \operatorname{asin}{\left(- \sin{\left(a \right)} \right)} + \pi$$
O
$$a + x = 2 \pi n - \operatorname{asin}{\left(\sin{\left(a \right)} \right)}$$
$$a + x = 2 \pi n + \operatorname{asin}{\left(\sin{\left(a \right)} \right)} + \pi$$
, donde n es cualquier número entero
Transportemos
$$a$$
al miembro derecho de la ecuación
con el signo opuesto, en total:
$$x = - a + 2 \pi n - \operatorname{asin}{\left(\sin{\left(a \right)} \right)}$$
$$x = - a + 2 \pi n + \operatorname{asin}{\left(\sin{\left(a \right)} \right)} + \pi$$
Gráfica
Respuesta rápida
[src]
x1 = -re(a) + I*(-im(a) + im(acos(-sin(a)))) + re(acos(-sin(a)))
$$x_{1} = i \left(- \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(\operatorname{acos}{\left(- \sin{\left(a \right)} \right)}\right)}\right) - \operatorname{re}{\left(a\right)} + \operatorname{re}{\left(\operatorname{acos}{\left(- \sin{\left(a \right)} \right)}\right)}$$
x2 = -re(a) - re(acos(-sin(a))) + 2*pi + I*(-im(a) - im(acos(-sin(a))))
$$x_{2} = i \left(- \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(\operatorname{acos}{\left(- \sin{\left(a \right)} \right)}\right)}\right) - \operatorname{re}{\left(a\right)} - \operatorname{re}{\left(\operatorname{acos}{\left(- \sin{\left(a \right)} \right)}\right)} + 2 \pi$$
x2 = i*(-im(a) - im(acos(-sin(a)))) - re(a) - re(acos(-sin(a))) + 2*pi
Suma y producto de raíces
[src]
suma
-re(a) + I*(-im(a) + im(acos(-sin(a)))) + re(acos(-sin(a))) + -re(a) - re(acos(-sin(a))) + 2*pi + I*(-im(a) - im(acos(-sin(a))))
$$\left(i \left(- \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(\operatorname{acos}{\left(- \sin{\left(a \right)} \right)}\right)}\right) - \operatorname{re}{\left(a\right)} + \operatorname{re}{\left(\operatorname{acos}{\left(- \sin{\left(a \right)} \right)}\right)}\right) + \left(i \left(- \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(\operatorname{acos}{\left(- \sin{\left(a \right)} \right)}\right)}\right) - \operatorname{re}{\left(a\right)} - \operatorname{re}{\left(\operatorname{acos}{\left(- \sin{\left(a \right)} \right)}\right)} + 2 \pi\right)$$
=
-2*re(a) + 2*pi + I*(-im(a) - im(acos(-sin(a)))) + I*(-im(a) + im(acos(-sin(a))))
$$i \left(- \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(\operatorname{acos}{\left(- \sin{\left(a \right)} \right)}\right)}\right) + i \left(- \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(\operatorname{acos}{\left(- \sin{\left(a \right)} \right)}\right)}\right) - 2 \operatorname{re}{\left(a\right)} + 2 \pi$$
producto
(-re(a) + I*(-im(a) + im(acos(-sin(a)))) + re(acos(-sin(a))))*(-re(a) - re(acos(-sin(a))) + 2*pi + I*(-im(a) - im(acos(-sin(a)))))
$$\left(i \left(- \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(\operatorname{acos}{\left(- \sin{\left(a \right)} \right)}\right)}\right) - \operatorname{re}{\left(a\right)} + \operatorname{re}{\left(\operatorname{acos}{\left(- \sin{\left(a \right)} \right)}\right)}\right) \left(i \left(- \operatorname{im}{\left(a\right)} - \operatorname{im}{\left(\operatorname{acos}{\left(- \sin{\left(a \right)} \right)}\right)}\right) - \operatorname{re}{\left(a\right)} - \operatorname{re}{\left(\operatorname{acos}{\left(- \sin{\left(a \right)} \right)}\right)} + 2 \pi\right)$$
=
(-re(acos(-sin(a))) + I*(-im(acos(-sin(a))) + im(a)) + re(a))*(-2*pi + I*(im(a) + im(acos(-sin(a)))) + re(a) + re(acos(-sin(a))))
$$\left(i \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(\operatorname{acos}{\left(- \sin{\left(a \right)} \right)}\right)}\right) + \operatorname{re}{\left(a\right)} - \operatorname{re}{\left(\operatorname{acos}{\left(- \sin{\left(a \right)} \right)}\right)}\right) \left(i \left(\operatorname{im}{\left(a\right)} + \operatorname{im}{\left(\operatorname{acos}{\left(- \sin{\left(a \right)} \right)}\right)}\right) + \operatorname{re}{\left(a\right)} + \operatorname{re}{\left(\operatorname{acos}{\left(- \sin{\left(a \right)} \right)}\right)} - 2 \pi\right)$$
(-re(acos(-sin(a))) + i*(-im(acos(-sin(a))) + im(a)) + re(a))*(-2*pi + i*(im(a) + im(acos(-sin(a)))) + re(a) + re(acos(-sin(a))))