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- La ecuación:
-
Ecuación x^2+4*x-32=0
-
Ecuación 9*x^2=0
-
Ecuación 4*x=24+x
-
Ecuación 16-7(5-x)=9
- 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(pi*sin(x))
- Derivada de:
-
-1
- Límite de la función:
-
-1
- Forma canónica:
- -1
-
Expresiones idénticas
- sin(pi*sin(x))=- uno
- seno de ( número pi multiplicar por seno de (x)) es igual a menos 1
- seno de ( número pi multiplicar por seno de (x)) es igual a menos uno
- sin(pisin(x))=-1
- sinpisinx=-1
-
Expresiones semejantes
- sin(pi*sin(x))=+1
- sin(pi*sinx)=-1
-
Expresiones con funciones
- Seno sin
- sin(x/4)^4-cos(x/4)^4=cos(x-pi/2)
- sin(x)=(2)/2
- sin(x)=1/√2
- sin(x)=1,2
- sin(cos(x))=(1/2)
- Seno sin
- sin(x/4)^4-cos(x/4)^4=cos(x-pi/2)
- sin(x)=(2)/2
- sin(x)=1/√2
- sin(x)=1,2
- sin(cos(x))=(1/2)
sin(pi*sin(x))=-1 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos la ecuación
$$\sin{\left(\pi \sin{\left(x \right)} \right)} = -1$$
cambiamos
$$\sin{\left(\pi \sin{\left(x \right)} \right)} + 1 = 0$$
$$\sin{\left(\pi \sin{\left(x \right)} \right)} + 1 = 0$$
Sustituimos
$$w = \sin{\left(\pi \sin{\left(x \right)} \right)}$$
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w = -1$$
Obtenemos la respuesta: w = -1
hacemos cambio inverso
$$\sin{\left(\pi \sin{\left(x \right)} \right)} = w$$
sustituimos w:
$$\sin{\left(\pi \sin{\left(x \right)} \right)} = -1$$
cambiamos
$$\sin{\left(\pi \sin{\left(x \right)} \right)} + 1 = 0$$
$$\sin{\left(\pi \sin{\left(x \right)} \right)} + 1 = 0$$
Sustituimos
$$w = \sin{\left(\pi \sin{\left(x \right)} \right)}$$
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w = -1$$
Obtenemos la respuesta: w = -1
hacemos cambio inverso
$$\sin{\left(\pi \sin{\left(x \right)} \right)} = w$$
sustituimos w:
Suma y producto de raíces
[src]
suma
pi 7*pi - -- + ---- + pi - re(asin(3/2)) - I*im(asin(3/2)) + I*im(asin(3/2)) + re(asin(3/2)) 6 6
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}\right) + \left(\left(- \frac{\pi}{6} + \frac{7 \pi}{6}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}\right)\right)$$
=
2*pi
$$2 \pi$$
producto
-pi 7*pi ----*----*(pi - re(asin(3/2)) - I*im(asin(3/2)))*(I*im(asin(3/2)) + re(asin(3/2))) 6 6
$$- \frac{\pi}{6} \frac{7 \pi}{6} \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}\right)$$
=
2
7*pi *(I*im(asin(3/2)) + re(asin(3/2)))*(-pi + I*im(asin(3/2)) + re(asin(3/2)))
-------------------------------------------------------------------------------
36
$$\frac{7 \pi^{2} \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}\right) \left(- \pi + \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}\right)}{36}$$
7*pi^2*(i*im(asin(3/2)) + re(asin(3/2)))*(-pi + i*im(asin(3/2)) + re(asin(3/2)))/36
Respuesta rápida
[src]
-pi
x1 = ----
6
$$x_{1} = - \frac{\pi}{6}$$
7*pi
x2 = ----
6
$$x_{2} = \frac{7 \pi}{6}$$
x3 = pi - re(asin(3/2)) - I*im(asin(3/2))
$$x_{3} = - \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}$$
x4 = I*im(asin(3/2)) + re(asin(3/2))
$$x_{4} = \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}$$
x4 = re(asin(3/2)) + i*im(asin(3/2))
Respuesta numérica
[src]
x1 = -59.1666617677488
x2 = -132.470489694285
x3 = 56.0250689535476
x4 = 85.3466004511484
x5 = 18.3259571008295
x6 = -13.0899690526506
x7 = 24.6091423484871
x8 = -63.3554519472469
x9 = 85.3465999673719
x10 = 53.9306739413208
x11 = -38.2227104657936
x12 = 3.66519153871422
x13 = -65.4498471137318
x14 = -0.523598600500097
x15 = 74.8746252321522
x16 = 93.7241810058253
x17 = -82.2050076241151
x18 = 60.2138592227626
x19 = 49.7418838491948
x20 = -34.0339203817864
x21 = 79.063415174746
x22 = -2.61799415622207
x23 = 43.4586985390256
x24 = 62.3082542599839
x25 = 91.629785835609
x26 = -78.0162175295362
x27 = 9.94837678070913
x28 = -90.5825882917856
x29 = 12.0427717675619
x30 = -25.6563400575784
x31 = 97.9129711005109
x32 = -71.73303245649
x33 = 87.4409956755458
x34 = 66.4970443581517
x35 = 68.5914394977552
x36 = 47.6474886875546
x37 = -78.0162175469491
x38 = -19.3731547998892
x39 = 30.8923281905739
x40 = -44.5058957424715
x41 = -88.4881928864687
x42 = -1133.59134884904
x43 = -31.9395254382276
x44 = 16.2315620577281
x45 = -84.2994027610386
x46 = -27.7507351061631
x47 = -15.184364636283
x48 = 28.7979324994445
x49 = -69.6386372153118
x50 = -21.467549956936
x51 = 22.5147472003714
x52 = -75.9218226841762
x53 = 5.75958669198159
x54 = -6.8067837124283
x55 = 72.7802296386064
x56 = -46.6002912131247
x57 = -40.3171056108353
x58 = 100.007366130042
x59 = -71.7330322692361
x60 = 816648.109121656
x61 = 41.3643028836498
x61 = 41.3643028836498
Gráfico