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- La ecuación:
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Ecuación x=(x+1)/2
- Ecuación (x-6)(-5x-9)=0
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Ecuación x^2-14*x+33=0
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Ecuación 5(x-4)=3x-10
- Expresar {x} en función de y en la ecuación:
- 12*x+1*y=15
- -17*x-12*y=-9
- 18*x+17*y=-14
- 16*x-17*y=-15
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Expresiones idénticas
- b=m*cos(t*w)
- b es igual a m multiplicar por coseno de (t multiplicar por w)
- b=mcos(tw)
- b=mcostw
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Expresiones con funciones
- Coseno cos
- cos(x)^(2)=cos(x)
- cos^2(x-1)=0
- cos(acos(x))=0
- cos(x)^(2)-cos(2*x)=0
- cos(t)=pi/3
b=m*cos(t*w) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos la ecuación
$$b = m \cos{\left(t w \right)}$$
es la ecuación trigonométrica más simple
La ecuación se convierte en
$$\cos{\left(t w \right)} = \frac{b}{m}$$
Esta ecuación se reorganiza en
$$t w = \pi n + \operatorname{acos}{\left(\frac{b}{m} \right)}$$
$$t w = \pi n + \operatorname{acos}{\left(\frac{b}{m} \right)} - \pi$$
O
$$t w = \pi n + \operatorname{acos}{\left(\frac{b}{m} \right)}$$
$$t w = \pi n + \operatorname{acos}{\left(\frac{b}{m} \right)} - \pi$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$t$$
obtenemos la respuesta:
$$w_{1} = \frac{\pi n + \operatorname{acos}{\left(\frac{b}{m} \right)}}{t}$$
$$w_{2} = \frac{\pi n + \operatorname{acos}{\left(\frac{b}{m} \right)} - \pi}{t}$$
$$b = m \cos{\left(t w \right)}$$
es la ecuación trigonométrica más simple
Dividamos ambos miembros de la ecuación en -m
La ecuación se convierte en
$$\cos{\left(t w \right)} = \frac{b}{m}$$
Esta ecuación se reorganiza en
$$t w = \pi n + \operatorname{acos}{\left(\frac{b}{m} \right)}$$
$$t w = \pi n + \operatorname{acos}{\left(\frac{b}{m} \right)} - \pi$$
O
$$t w = \pi n + \operatorname{acos}{\left(\frac{b}{m} \right)}$$
$$t w = \pi n + \operatorname{acos}{\left(\frac{b}{m} \right)} - \pi$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$t$$
obtenemos la respuesta:
$$w_{1} = \frac{\pi n + \operatorname{acos}{\left(\frac{b}{m} \right)}}{t}$$
$$w_{2} = \frac{\pi n + \operatorname{acos}{\left(\frac{b}{m} \right)} - \pi}{t}$$
Gráfica
Respuesta rápida
[src]
/ / / /b\\ \ / /b\\ \ / / /b\\ \ / /b\\
| |- re|acos|-|| + 2*pi|*im(t) im|acos|-||*re(t)| |- re|acos|-|| + 2*pi|*re(t) im(t)*im|acos|-||
| \ \ \m// / \ \m// | \ \ \m// / \ \m//
w1 = I*|- ---------------------------- - -----------------| + ---------------------------- - -----------------
| 2 2 2 2 | 2 2 2 2
\ im (t) + re (t) im (t) + re (t) / im (t) + re (t) im (t) + re (t)
$$w_{1} = i \left(- \frac{\left(- \operatorname{re}{\left(\operatorname{acos}{\left(\frac{b}{m} \right)}\right)} + 2 \pi\right) \operatorname{im}{\left(t\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}} - \frac{\operatorname{re}{\left(t\right)} \operatorname{im}{\left(\operatorname{acos}{\left(\frac{b}{m} \right)}\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}}\right) + \frac{\left(- \operatorname{re}{\left(\operatorname{acos}{\left(\frac{b}{m} \right)}\right)} + 2 \pi\right) \operatorname{re}{\left(t\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}} - \frac{\operatorname{im}{\left(t\right)} \operatorname{im}{\left(\operatorname{acos}{\left(\frac{b}{m} \right)}\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}}$$
/ /b\\ / /b\\
|acos|-|| |acos|-||
| \m/| | \m/|
w2 = I*im|-------| + re|-------|
\ t / \ t /
$$w_{2} = \operatorname{re}{\left(\frac{\operatorname{acos}{\left(\frac{b}{m} \right)}}{t}\right)} + i \operatorname{im}{\left(\frac{\operatorname{acos}{\left(\frac{b}{m} \right)}}{t}\right)}$$
w2 = re(acos(b/m)/t) + i*im(acos(b/m)/t)
Suma y producto de raíces
[src]
suma
/ / / /b\\ \ / /b\\ \ / / /b\\ \ / /b\\ / /b\\ / /b\\ | |- re|acos|-|| + 2*pi|*im(t) im|acos|-||*re(t)| |- re|acos|-|| + 2*pi|*re(t) im(t)*im|acos|-|| |acos|-|| |acos|-|| | \ \ \m// / \ \m// | \ \ \m// / \ \m// | \m/| | \m/| I*|- ---------------------------- - -----------------| + ---------------------------- - ----------------- + I*im|-------| + re|-------| | 2 2 2 2 | 2 2 2 2 \ t / \ t / \ im (t) + re (t) im (t) + re (t) / im (t) + re (t) im (t) + re (t)
$$\left(\operatorname{re}{\left(\frac{\operatorname{acos}{\left(\frac{b}{m} \right)}}{t}\right)} + i \operatorname{im}{\left(\frac{\operatorname{acos}{\left(\frac{b}{m} \right)}}{t}\right)}\right) + \left(i \left(- \frac{\left(- \operatorname{re}{\left(\operatorname{acos}{\left(\frac{b}{m} \right)}\right)} + 2 \pi\right) \operatorname{im}{\left(t\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}} - \frac{\operatorname{re}{\left(t\right)} \operatorname{im}{\left(\operatorname{acos}{\left(\frac{b}{m} \right)}\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}}\right) + \frac{\left(- \operatorname{re}{\left(\operatorname{acos}{\left(\frac{b}{m} \right)}\right)} + 2 \pi\right) \operatorname{re}{\left(t\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}} - \frac{\operatorname{im}{\left(t\right)} \operatorname{im}{\left(\operatorname{acos}{\left(\frac{b}{m} \right)}\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}}\right)$$
=
/ / / /b\\ \ / /b\\ \ / /b\\ / / /b\\ \ / /b\\ / /b\\ | |- re|acos|-|| + 2*pi|*im(t) im|acos|-||*re(t)| |acos|-|| |- re|acos|-|| + 2*pi|*re(t) im(t)*im|acos|-|| |acos|-|| | \ \ \m// / \ \m// | | \m/| \ \ \m// / \ \m// | \m/| I*|- ---------------------------- - -----------------| + I*im|-------| + ---------------------------- - ----------------- + re|-------| | 2 2 2 2 | \ t / 2 2 2 2 \ t / \ im (t) + re (t) im (t) + re (t) / im (t) + re (t) im (t) + re (t)
$$i \left(- \frac{\left(- \operatorname{re}{\left(\operatorname{acos}{\left(\frac{b}{m} \right)}\right)} + 2 \pi\right) \operatorname{im}{\left(t\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}} - \frac{\operatorname{re}{\left(t\right)} \operatorname{im}{\left(\operatorname{acos}{\left(\frac{b}{m} \right)}\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}}\right) + \operatorname{re}{\left(\frac{\operatorname{acos}{\left(\frac{b}{m} \right)}}{t}\right)} + i \operatorname{im}{\left(\frac{\operatorname{acos}{\left(\frac{b}{m} \right)}}{t}\right)} + \frac{\left(- \operatorname{re}{\left(\operatorname{acos}{\left(\frac{b}{m} \right)}\right)} + 2 \pi\right) \operatorname{re}{\left(t\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}} - \frac{\operatorname{im}{\left(t\right)} \operatorname{im}{\left(\operatorname{acos}{\left(\frac{b}{m} \right)}\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}}$$
producto
/ / / / /b\\ \ / /b\\ \ / / /b\\ \ / /b\\\ / / /b\\ / /b\\\ | | |- re|acos|-|| + 2*pi|*im(t) im|acos|-||*re(t)| |- re|acos|-|| + 2*pi|*re(t) im(t)*im|acos|-||| | |acos|-|| |acos|-||| | | \ \ \m// / \ \m// | \ \ \m// / \ \m//| | | \m/| | \m/|| |I*|- ---------------------------- - -----------------| + ---------------------------- - -----------------|*|I*im|-------| + re|-------|| | | 2 2 2 2 | 2 2 2 2 | \ \ t / \ t // \ \ im (t) + re (t) im (t) + re (t) / im (t) + re (t) im (t) + re (t) /
$$\left(\operatorname{re}{\left(\frac{\operatorname{acos}{\left(\frac{b}{m} \right)}}{t}\right)} + i \operatorname{im}{\left(\frac{\operatorname{acos}{\left(\frac{b}{m} \right)}}{t}\right)}\right) \left(i \left(- \frac{\left(- \operatorname{re}{\left(\operatorname{acos}{\left(\frac{b}{m} \right)}\right)} + 2 \pi\right) \operatorname{im}{\left(t\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}} - \frac{\operatorname{re}{\left(t\right)} \operatorname{im}{\left(\operatorname{acos}{\left(\frac{b}{m} \right)}\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}}\right) + \frac{\left(- \operatorname{re}{\left(\operatorname{acos}{\left(\frac{b}{m} \right)}\right)} + 2 \pi\right) \operatorname{re}{\left(t\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}} - \frac{\operatorname{im}{\left(t\right)} \operatorname{im}{\left(\operatorname{acos}{\left(\frac{b}{m} \right)}\right)}}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}}\right)$$
=
/ / /b\\ / /b\\\
| |acos|-|| |acos|-|||
| | \m/| | \m/|| // / /b\\\ / /b\\ // / /b\\\ / /b\\ \\
-|I*im|-------| + re|-------||*||-2*pi + re|acos|-|||*re(t) + im(t)*im|acos|-|| - I*||-2*pi + re|acos|-|||*im(t) - im|acos|-||*re(t)||
\ \ t / \ t // \\ \ \m/// \ \m// \\ \ \m/// \ \m// //
---------------------------------------------------------------------------------------------------------------------------------------
2 2
im (t) + re (t)
$$- \frac{\left(\operatorname{re}{\left(\frac{\operatorname{acos}{\left(\frac{b}{m} \right)}}{t}\right)} + i \operatorname{im}{\left(\frac{\operatorname{acos}{\left(\frac{b}{m} \right)}}{t}\right)}\right) \left(- i \left(\left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{b}{m} \right)}\right)} - 2 \pi\right) \operatorname{im}{\left(t\right)} - \operatorname{re}{\left(t\right)} \operatorname{im}{\left(\operatorname{acos}{\left(\frac{b}{m} \right)}\right)}\right) + \left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{b}{m} \right)}\right)} - 2 \pi\right) \operatorname{re}{\left(t\right)} + \operatorname{im}{\left(t\right)} \operatorname{im}{\left(\operatorname{acos}{\left(\frac{b}{m} \right)}\right)}\right)}{\left(\operatorname{re}{\left(t\right)}\right)^{2} + \left(\operatorname{im}{\left(t\right)}\right)^{2}}$$
-(i*im(acos(b/m)/t) + re(acos(b/m)/t))*((-2*pi + re(acos(b/m)))*re(t) + im(t)*im(acos(b/m)) - i*((-2*pi + re(acos(b/m)))*im(t) - im(acos(b/m))*re(t)))/(im(t)^2 + re(t)^2)