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- La ecuación:
-
Ecuación x+(8-3x)=12
-
Ecuación x=(x+1)/2
-
Ecuación 350-(45+a)=60
-
Ecuación x^x=x
- Expresar {x} en función de y en la ecuación:
- 15*x-5*y=-5
- 11*x-12*y=11
- 8*x-13*y=-12
- 19*x-2*y=-17
- Gráfico de la función y =:
-
sin(cos(x))
- Integral de d{x}:
- sin(cos(x))
- Derivada de:
-
sin(cos(x))
-
(1/2)
- Suma de la serie:
-
(1/2)
-
Expresiones idénticas
- sin(cos(x))=(uno / dos)
- seno de ( coseno de (x)) es igual a (1 dividir por 2)
- seno de ( coseno de (x)) es igual a (uno dividir por dos)
- sincosx=1/2
- sin(cos(x))=(1 dividir por 2)
-
Expresiones semejantes
- (((5*sin(cos(x^2)+exp(tan(x))))/log(x))+Abs(cos(x)-sin(x)))/3=0
- sin(x+pi/4)^2=cos(x)+1/2
- x=(x+1)/2
- 1/(2*x-11)=1/3
- sin^2(x)-sincos(x)-2cos^2x=0
- sin(cosx)=(1/2)
-
Expresiones con funciones
- Seno sin
- sin(x/4)^4-cos(x/4)^4=cos(x-pi/2)
- sin(x)=(2)/2
- sin(pi*sin(x))=-1
- sin(x)=1/√2
- sin(x)=1,2
- Coseno cos
- cos(x)=(1/√2)
- cos(0.01*x^4+3)=0
- cos(x)+sin(3x)=0
- cos(x)=-1_2
- cos^2(x)=(abs(2x))/pi
sin(cos(x))=(1/2) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos la ecuación
$$\sin{\left(\cos{\left(x \right)} \right)} = \frac{1}{2}$$
cambiamos
$$\sin{\left(\cos{\left(x \right)} \right)} - \frac{1}{2} = 0$$
$$\sin{\left(\cos{\left(x \right)} \right)} - \frac{1}{2} = 0$$
Sustituimos
$$w = \sin{\left(\cos{\left(x \right)} \right)}$$
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w = \frac{1}{2}$$
Obtenemos la respuesta: w = 1/2
hacemos cambio inverso
$$\sin{\left(\cos{\left(x \right)} \right)} = w$$
sustituimos w:
$$\sin{\left(\cos{\left(x \right)} \right)} = \frac{1}{2}$$
cambiamos
$$\sin{\left(\cos{\left(x \right)} \right)} - \frac{1}{2} = 0$$
$$\sin{\left(\cos{\left(x \right)} \right)} - \frac{1}{2} = 0$$
Sustituimos
$$w = \sin{\left(\cos{\left(x \right)} \right)}$$
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w = \frac{1}{2}$$
Obtenemos la respuesta: w = 1/2
hacemos cambio inverso
$$\sin{\left(\cos{\left(x \right)} \right)} = w$$
sustituimos w:
Suma y producto de raíces
[src]
suma
/pi\ /pi\ / /5*pi\\ / /5*pi\\ / /5*pi\\
- acos|--| + 2*pi + acos|--| + 2*pi - I*im|acos|----|| + I*im|acos|----|| + re|acos|----||
\6 / \6 / \ \ 6 // \ \ 6 // \ \ 6 //
$$\left(\left(\operatorname{acos}{\left(\frac{\pi}{6} \right)} + \left(- \operatorname{acos}{\left(\frac{\pi}{6} \right)} + 2 \pi\right)\right) + \left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{5 \pi}{6} \right)}\right)}\right)\right) + \left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{5 \pi}{6} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{5 \pi}{6} \right)}\right)}\right)$$
=
/ /5*pi\\
4*pi + re|acos|----||
\ \ 6 //
$$\operatorname{re}{\left(\operatorname{acos}{\left(\frac{5 \pi}{6} \right)}\right)} + 4 \pi$$
producto
/ /pi\ \ /pi\ / / /5*pi\\\ / / /5*pi\\ / /5*pi\\\ |- acos|--| + 2*pi|*acos|--|*|2*pi - I*im|acos|----|||*|I*im|acos|----|| + re|acos|----||| \ \6 / / \6 / \ \ \ 6 /// \ \ \ 6 // \ \ 6 ///
$$\left(- \operatorname{acos}{\left(\frac{\pi}{6} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{\pi}{6} \right)} \left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{5 \pi}{6} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{5 \pi}{6} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{5 \pi}{6} \right)}\right)}\right)$$
=
/ /pi\ \ / / /5*pi\\\ / / /5*pi\\ / /5*pi\\\ /pi\ |- acos|--| + 2*pi|*|2*pi - I*im|acos|----|||*|I*im|acos|----|| + re|acos|----|||*acos|--| \ \6 / / \ \ \ 6 /// \ \ \ 6 // \ \ 6 /// \6 /
$$\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{5 \pi}{6} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{5 \pi}{6} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{5 \pi}{6} \right)}\right)}\right) \left(- \operatorname{acos}{\left(\frac{\pi}{6} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{\pi}{6} \right)}$$
(-acos(pi/6) + 2*pi)*(2*pi - i*im(acos(5*pi/6)))*(i*im(acos(5*pi/6)) + re(acos(5*pi/6)))*acos(pi/6)
Respuesta rápida
[src]
/pi\
x1 = - acos|--| + 2*pi
\6 /
$$x_{1} = - \operatorname{acos}{\left(\frac{\pi}{6} \right)} + 2 \pi$$
/pi\
x2 = acos|--|
\6 /
$$x_{2} = \operatorname{acos}{\left(\frac{\pi}{6} \right)}$$
/ /5*pi\\
x3 = 2*pi - I*im|acos|----||
\ \ 6 //
$$x_{3} = 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{5 \pi}{6} \right)}\right)}$$
/ /5*pi\\ / /5*pi\\
x4 = I*im|acos|----|| + re|acos|----||
\ \ 6 // \ \ 6 //
$$x_{4} = \operatorname{re}{\left(\operatorname{acos}{\left(\frac{5 \pi}{6} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{5 \pi}{6} \right)}\right)}$$
x4 = re(acos(5*pi/6)) + i*im(acos(5*pi/6))
Respuesta numérica
[src]
x1 = 86.9448675568188
x2 = -55.5289410209208
x3 = 13.5860973580546
x4 = -1521.55057108116
x5 = -93.2280528639983
x6 = 55.5289410209208
x7 = 17.8298291778433
x8 = 11.5466438706637
x9 = -45.0020238939526
x10 = 19.8692826652342
x11 = 24.1130144850229
x12 = -24.1130144850229
x13 = 42.9625704065617
x14 = -13.5860973580546
x15 = -51.2852092011321
x16 = 51.2852092011321
x17 = -7.30291205087504
x18 = -26.1524679724138
x19 = 74.3784969424596
x20 = -1.01972674369545
x21 = -63.8515798154913
x22 = -38.718838586773
x23 = -5.26345856348414
x24 = 80.6616822496392
x25 = -76.4179504298505
x26 = 36.6793850993821
x27 = 5.26345856348414
x28 = -32.4356532795934
x29 = 61.8121263281004
x30 = 82.7011357370301
x31 = 70.1347651226709
x32 = 49.2457557137412
x33 = -176.948915344724
x34 = 3781.45782817842
x35 = -61.8121263281004
x36 = -68.09531163528
x37 = -264.913509645238
x38 = -19.8692826652342
x39 = 95.2675063513892
x40 = -95.2675063513892
x41 = 32.4356532795934
x42 = 88.9843210442097
x43 = -11.5466438706637
x44 = -70.1347651226709
x45 = 7.30291205087504
x46 = 1.01972674369545
x47 = 63.8515798154913
x48 = -74.3784969424596
x49 = -99.5112381711779
x50 = 45.0020238939526
x51 = 26.1524679724138
x52 = -457.652800680414
x53 = 68.09531163528
x54 = 93.2280528639983
x55 = 38.718838586773
x56 = -42.9625704065617
x57 = -80.6616822496392
x58 = -17.8298291778433
x59 = -36.6793850993821
x60 = -88.9843210442097
x61 = -30.3961997922025
x62 = -82.7011357370301
x63 = 30.3961997922025
x64 = -57.5683945083117
x65 = 57.5683945083117
x66 = -49.2457557137412
x67 = 99.5112381711779
x68 = 76.4179504298505
x69 = -86.9448675568188
x69 = -86.9448675568188
Gráfico