Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación 2*(x+2)*(x+4)=x^2+2*x
-
Ecuación 2*(1-3*x)/3+(3*x-3)/2=(x-3)/6-1
-
Ecuación (3*x+4)/(x^2-16)=x^2/(x^2-16)
-
Ecuación x^4+3*x^2-10=0
- Expresar {x} en función de y en la ecuación:
- -17*x+9*y=-18
- -19*x-4*y=5
- -8*x-1*y=9
- 4*x+4*y=13
- Derivada de:
-
2*sin(x)
- Integral de d{x}:
- 2*sin(x)
- Límite de la función:
-
2*sin(x)
-
Expresiones idénticas
- sin(x)^ dos - tres = dos *sin(x)
- seno de (x) al cuadrado menos 3 es igual a 2 multiplicar por seno de (x)
- seno de (x) en el grado dos menos tres es igual a dos multiplicar por seno de (x)
- sin(x)2-3=2*sin(x)
- sinx2-3=2*sinx
- sin(x)²-3=2*sin(x)
- sin(x) en el grado 2-3=2*sin(x)
- sin(x)^2-3=2sin(x)
- sin(x)2-3=2sin(x)
- sinx2-3=2sinx
- sinx^2-3=2sinx
-
Expresiones semejantes
- sin(x)^2+3=2*sin(x)
- (2*sinx-1)/(sqrt(cosx))=0
- log(3sin2x−2sinx−3cosx+4)/log(3)=1
- (cos-1\2)(sinx+1)=0
- sinx^2-3=2*sinx
-
Expresiones con funciones
- Seno sin
- sin(8*x)=sin(x)
- sin((p+2*x)/3)=sin((-2*p+x)/3)
- sin(pi*x)/12=-(1/2)
- sin(pix)=1/2
- sin4x=-√2÷2
- Seno sin
- sin(8*x)=sin(x)
- sin((p+2*x)/3)=sin((-2*p+x)/3)
- sin(pi*x)/12=-(1/2)
- sin(pix)=1/2
- sin4x=-√2÷2
sin(x)^2-3=2*sin(x) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 sin (x) - 3 = 2*sin(x)
$$\sin^{2}{\left(x \right)} - 3 = 2 \sin{\left(x \right)}$$
Solución detallada
Tenemos la ecuación
$$\sin^{2}{\left(x \right)} - 3 = 2 \sin{\left(x \right)}$$
cambiamos
$$\sin^{2}{\left(x \right)} - 2 \sin{\left(x \right)} - 3 = 0$$
$$\left(\sin^{2}{\left(x \right)} - 3\right) - 2 \sin{\left(x \right)} = 0$$
Sustituimos
$$w = \sin{\left(x \right)}$$
Es la ecuación de la forma
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$w_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$w_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = 1$$
$$b = -2$$
$$c = -3$$
, entonces
Como D > 0 la ecuación tiene dos raíces.
o
$$w_{1} = 3$$
$$w_{2} = -1$$
hacemos cambio inverso
$$\sin{\left(x \right)} = w$$
Tenemos la ecuación
$$\sin{\left(x \right)} = w$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
O
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
, donde n es cualquier número entero
sustituimos w:
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(w_{1} \right)}$$
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(3 \right)}$$
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(3 \right)}$$
$$x_{2} = 2 \pi n + \operatorname{asin}{\left(w_{2} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{asin}{\left(-1 \right)}$$
$$x_{2} = 2 \pi n - \frac{\pi}{2}$$
$$x_{3} = 2 \pi n - \operatorname{asin}{\left(w_{1} \right)} + \pi$$
$$x_{3} = 2 \pi n + \pi - \operatorname{asin}{\left(3 \right)}$$
$$x_{3} = 2 \pi n + \pi - \operatorname{asin}{\left(3 \right)}$$
$$x_{4} = 2 \pi n - \operatorname{asin}{\left(w_{2} \right)} + \pi$$
$$x_{4} = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi$$
$$x_{4} = 2 \pi n + \frac{3 \pi}{2}$$
$$\sin^{2}{\left(x \right)} - 3 = 2 \sin{\left(x \right)}$$
cambiamos
$$\sin^{2}{\left(x \right)} - 2 \sin{\left(x \right)} - 3 = 0$$
$$\left(\sin^{2}{\left(x \right)} - 3\right) - 2 \sin{\left(x \right)} = 0$$
Sustituimos
$$w = \sin{\left(x \right)}$$
Es la ecuación de la forma
a*w^2 + b*w + c = 0
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$w_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$w_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = 1$$
$$b = -2$$
$$c = -3$$
, entonces
D = b^2 - 4 * a * c =
(-2)^2 - 4 * (1) * (-3) = 16
Como D > 0 la ecuación tiene dos raíces.
w1 = (-b + sqrt(D)) / (2*a)
w2 = (-b - sqrt(D)) / (2*a)
o
$$w_{1} = 3$$
$$w_{2} = -1$$
hacemos cambio inverso
$$\sin{\left(x \right)} = w$$
Tenemos la ecuación
$$\sin{\left(x \right)} = w$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
O
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
, donde n es cualquier número entero
sustituimos w:
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(w_{1} \right)}$$
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(3 \right)}$$
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(3 \right)}$$
$$x_{2} = 2 \pi n + \operatorname{asin}{\left(w_{2} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{asin}{\left(-1 \right)}$$
$$x_{2} = 2 \pi n - \frac{\pi}{2}$$
$$x_{3} = 2 \pi n - \operatorname{asin}{\left(w_{1} \right)} + \pi$$
$$x_{3} = 2 \pi n + \pi - \operatorname{asin}{\left(3 \right)}$$
$$x_{3} = 2 \pi n + \pi - \operatorname{asin}{\left(3 \right)}$$
$$x_{4} = 2 \pi n - \operatorname{asin}{\left(w_{2} \right)} + \pi$$
$$x_{4} = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi$$
$$x_{4} = 2 \pi n + \frac{3 \pi}{2}$$
Respuesta rápida
[src]
-pi
x1 = ----
2
$$x_{1} = - \frac{\pi}{2}$$
3*pi
x2 = ----
2
$$x_{2} = \frac{3 \pi}{2}$$
x3 = pi - re(asin(3)) - I*im(asin(3))
$$x_{3} = - \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}$$
x4 = I*im(asin(3)) + re(asin(3))
$$x_{4} = \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}$$
x4 = re(asin(3)) + i*im(asin(3))
Suma y producto de raíces
[src]
suma
pi 3*pi - -- + ---- + pi - re(asin(3)) - I*im(asin(3)) + I*im(asin(3)) + re(asin(3)) 2 2
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right) + \left(\left(- \frac{\pi}{2} + \frac{3 \pi}{2}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right)\right)$$
=
2*pi
$$2 \pi$$
producto
-pi 3*pi ----*----*(pi - re(asin(3)) - I*im(asin(3)))*(I*im(asin(3)) + re(asin(3))) 2 2
$$- \frac{\pi}{2} \frac{3 \pi}{2} \left(- \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right)$$
=
2
3*pi *(I*im(asin(3)) + re(asin(3)))*(-pi + I*im(asin(3)) + re(asin(3)))
-----------------------------------------------------------------------
4
$$\frac{3 \pi^{2} \left(\operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right) \left(- \pi + \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right)}{4}$$
3*pi^2*(i*im(asin(3)) + re(asin(3)))*(-pi + i*im(asin(3)) + re(asin(3)))/4
Respuesta numérica
[src]
x1 = 92.6769835070253
x2 = -39.2699079075865
x3 = 92.6769830689412
x4 = 73.8274274813446
x5 = 10.9955746230205
x6 = -7.85398149759801
x7 = 17.2787599090696
x8 = -164.933614398177
x9 = 29.8451303217623
x10 = -89.5353907485116
x11 = 10.9955739814993
x12 = 42.4115009058131
x13 = 73.827427591263
x14 = 117.809725233756
x15 = 4.71238875528975
x16 = -39.2699076412407
x17 = -14.1371668194089
x18 = -1.57079653638307
x19 = 48.6946859120413
x20 = -32.9867231721691
x21 = 67.5442418055755
x22 = 54.9778717720118
x23 = 86.3937976360352
x24 = -95.8185758680893
x25 = -14.1371665766936
x26 = -45.5530935897427
x27 = -70.6858350312864
x28 = -45.5530936309972
x29 = -26.7035372446302
x30 = -70.6858343985417
x31 = 86.3937978876249
x32 = 48.6946863700612
x33 = 212.057503588662
x34 = 42.4115007283113
x35 = 67.5442422944741
x36 = -51.8362786895378
x37 = -83.2522051037983
x38 = -58.119463652249
x39 = 17.2787592660486
x40 = 80.1106131400977
x41 = 4.71238923181769
x42 = -76.9690203256113
x43 = -108.38494727522
x44 = 98.9601682894894
x45 = -64.4026491754768
x46 = 23.5619446676752
x47 = 29.845130504401
x48 = -64.4026496039382
x49 = -20.4203520186622
x50 = 882955.610865625
x51 = -89.5353907308516
x52 = -76.9690196760468
x53 = 61.261057062553
x54 = 98.9601689206173
x55 = 23.5619451379884
x56 = -133.517687838813
x57 = -139.800873467486
x58 = 4.71238886235498
x59 = 36.1283157033748
x60 = -1.57079643080582
x61 = -26.703537882833
x62 = 42.4115005526819
x63 = 54.9778711353875
x64 = -58.1194639985047
x65 = -83.2522055577573
x66 = -39.2699084013107
x67 = -14.1371668381663
x68 = -32.9867225263379
x69 = -83.2522050480464
x70 = 61.2610564153358
x71 = -20.4203524688757
x71 = -20.4203524688757