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Otras calculadoras
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- La ecuación:
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Ecuación 9-7(x+3)=5-6x
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Ecuación 2x-4=8+2x
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Ecuación 2,4(x+0,98)=4,08
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Ecuación 7x=-30+2x
- Expresar {x} en función de y en la ecuación:
- 4*x+8*y=7
- -1*x+4*y=-10
- -16*x+10*y=-11
- 15*x+12*y=-19
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Expresiones idénticas
- (a- dos)*sin(x)+cos(x)=a
- (a menos 2) multiplicar por seno de (x) más coseno de (x) es igual a a
- (a menos dos) multiplicar por seno de (x) más coseno de (x) es igual a a
- (a-2)sin(x)+cos(x)=a
- a-2sinx+cosx=a
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Expresiones semejantes
- (a-2)*sin(x)-cos(x)=a
- (a+2)*sin(x)+cos(x)=a
- (a-2)*sinx+cosx=a
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Expresiones con funciones
- Seno sin
- sin(x)=-4
- sin(3*x-pi/4)=sqrt(3)/2
- sin(x)=10
- sin(x)=2/7
- sin(x)=x
- Coseno cos
- cos(x)=-1,1
- cos(pi*x)/(x-2)=1/(x-2)
- cos(x+pi/2)=sqrt(3)/2
- cos(x)=(2)/2
- cos(3*x-pi/4)=1
(a-2)*sin(x)+cos(x)=a la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
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(a - 2)*sin(x) + cos(x) = a
$$\left(a - 2\right) \sin{\left(x \right)} + \cos{\left(x \right)} = a$$
Gráfica
Respuesta rápida
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/ / _________ \\ / / _________ \\
| |2 + \/ 5 - 4*a - a|| | |2 + \/ 5 - 4*a - a||
x1 = - 2*re|atan|-------------------|| - 2*I*im|atan|-------------------||
\ \ 1 + a // \ \ 1 + a //
$$x_{1} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{- a + \sqrt{5 - 4 a} + 2}{a + 1} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{- a + \sqrt{5 - 4 a} + 2}{a + 1} \right)}\right)}$$
/ / _________\\ / / _________\\
| |-2 + a + \/ 5 - 4*a || | |-2 + a + \/ 5 - 4*a ||
x2 = 2*re|atan|--------------------|| + 2*I*im|atan|--------------------||
\ \ 1 + a // \ \ 1 + a //
$$x_{2} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{a + \sqrt{5 - 4 a} - 2}{a + 1} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{a + \sqrt{5 - 4 a} - 2}{a + 1} \right)}\right)}$$
x2 = 2*re(atan((a + sqrt(5 - 4*a) - 2)/(a + 1))) + 2*i*im(atan((a + sqrt(5 - 4*a) - 2)/(a + 1)))
Suma y producto de raíces
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suma
/ / _________ \\ / / _________ \\ / / _________\\ / / _________\\
| |2 + \/ 5 - 4*a - a|| | |2 + \/ 5 - 4*a - a|| | |-2 + a + \/ 5 - 4*a || | |-2 + a + \/ 5 - 4*a ||
- 2*re|atan|-------------------|| - 2*I*im|atan|-------------------|| + 2*re|atan|--------------------|| + 2*I*im|atan|--------------------||
\ \ 1 + a // \ \ 1 + a // \ \ 1 + a // \ \ 1 + a //
$$\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{- a + \sqrt{5 - 4 a} + 2}{a + 1} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{- a + \sqrt{5 - 4 a} + 2}{a + 1} \right)}\right)}\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{a + \sqrt{5 - 4 a} - 2}{a + 1} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{a + \sqrt{5 - 4 a} - 2}{a + 1} \right)}\right)}\right)$$
=
/ / _________ \\ / / _________\\ / / _________ \\ / / _________\\
| |2 + \/ 5 - 4*a - a|| | |-2 + a + \/ 5 - 4*a || | |2 + \/ 5 - 4*a - a|| | |-2 + a + \/ 5 - 4*a ||
- 2*re|atan|-------------------|| + 2*re|atan|--------------------|| - 2*I*im|atan|-------------------|| + 2*I*im|atan|--------------------||
\ \ 1 + a // \ \ 1 + a // \ \ 1 + a // \ \ 1 + a //
$$- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{- a + \sqrt{5 - 4 a} + 2}{a + 1} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{a + \sqrt{5 - 4 a} - 2}{a + 1} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{- a + \sqrt{5 - 4 a} + 2}{a + 1} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{a + \sqrt{5 - 4 a} - 2}{a + 1} \right)}\right)}$$
producto
/ / / _________ \\ / / _________ \\\ / / / _________\\ / / _________\\\ | | |2 + \/ 5 - 4*a - a|| | |2 + \/ 5 - 4*a - a||| | | |-2 + a + \/ 5 - 4*a || | |-2 + a + \/ 5 - 4*a ||| |- 2*re|atan|-------------------|| - 2*I*im|atan|-------------------|||*|2*re|atan|--------------------|| + 2*I*im|atan|--------------------||| \ \ \ 1 + a // \ \ 1 + a /// \ \ \ 1 + a // \ \ 1 + a ///
$$\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{- a + \sqrt{5 - 4 a} + 2}{a + 1} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{- a + \sqrt{5 - 4 a} + 2}{a + 1} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{a + \sqrt{5 - 4 a} - 2}{a + 1} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{a + \sqrt{5 - 4 a} - 2}{a + 1} \right)}\right)}\right)$$
=
/ / / _________\\ / / _________\\\ / / / _________ \\ / / _________ \\\ | | |-2 + a + \/ 5 - 4*a || | |-2 + a + \/ 5 - 4*a ||| | | |2 + \/ 5 - 4*a - a|| | |2 + \/ 5 - 4*a - a||| -4*|I*im|atan|--------------------|| + re|atan|--------------------|||*|I*im|atan|-------------------|| + re|atan|-------------------||| \ \ \ 1 + a // \ \ 1 + a /// \ \ \ 1 + a // \ \ 1 + a ///
$$- 4 \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{- a + \sqrt{5 - 4 a} + 2}{a + 1} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{- a + \sqrt{5 - 4 a} + 2}{a + 1} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{a + \sqrt{5 - 4 a} - 2}{a + 1} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{a + \sqrt{5 - 4 a} - 2}{a + 1} \right)}\right)}\right)$$
-4*(i*im(atan((-2 + a + sqrt(5 - 4*a))/(1 + a))) + re(atan((-2 + a + sqrt(5 - 4*a))/(1 + a))))*(i*im(atan((2 + sqrt(5 - 4*a) - a)/(1 + a))) + re(atan((2 + sqrt(5 - 4*a) - a)/(1 + a))))