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La ecuación:
Ecuación x+4=0
Ecuación x*(x^2+8*x+16)=5*(x+4)
Ecuación 7+8x=-2x-5
Ecuación ((57.6/(150-x))^0.15)*((150+x)+10)/171.712=1
Expresar {x} en función de y en la ecuación:
18*x-11*y=2
-18*x-2*y=9
-9*x+1*y=3
9*x+10*y=5
Expresiones idénticas
2sin^2x+cos^2x-3sinx- cinco = cero
2 seno de al cuadrado x más coseno de al cuadrado x menos 3 seno de x menos 5 es igual a 0
2 seno de al cuadrado x más coseno de al cuadrado x menos 3 seno de x menos cinco es igual a cero
2sin2x+cos2x-3sinx-5=0
2sin²x+cos²x-3sinx-5=0
2sin en el grado 2x+cos en el grado 2x-3sinx-5=0
2sin^2x+cos^2x-3sinx-5=O
Expresiones semejantes
2sin^2x+cos^2x+3sinx-5=0
2sin^2x+cos^2x-3sinx+5=0
2sin^2x-cos^2x-3sinx-5=0
Expresiones con funciones
Coseno cos
cos2x=1/2
cos(pi+x)=1/2
cos(4*x)=0
cos(x)=-3
cos(2x)=1

2sin^2x+cos^2x-3sinx-5=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

     2         2                      
2*sin (x) + cos (x) - 3*sin(x) - 5 = 0

\left(\left(2 \sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right) - 3 \sin{\left(x \right)}\right) - 5 = 0

Simplificar

Solución detallada

Tenemos la ecuación

\left(\left(2 \sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right) - 3 \sin{\left(x \right)}\right) - 5 = 0

cambiamos

\sin^{2}{\left(x \right)} - 3 \sin{\left(x \right)} - 4 = 0

\sin^{2}{\left(x \right)} - 3 \sin{\left(x \right)} - 4 = 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 = -3

c = -4

, entonces

D = b^2 - 4 * a * c =

(-3)^2 - 4 * (1) * (-4) = 25

Como D > 0 la ecuación tiene dos raíces.

w1 = (-b + sqrt(D)) / (2*a)

w2 = (-b - sqrt(D)) / (2*a)

w_{1} = 4

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

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(4 \right)}

x_{1} = 2 \pi n + \operatorname{asin}{\left(4 \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(4 \right)}

x_{3} = 2 \pi n + \pi - \operatorname{asin}{\left(4 \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}

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Suma y producto de raíces [src]

suma

           /    /        ____\\         /    /        ____\\       /    /        ____\\         /    /        ____\\
  pi       |    |1   I*\/ 15 ||         |    |1   I*\/ 15 ||       |    |1   I*\/ 15 ||         |    |1   I*\/ 15 ||
- -- + 2*re|atan|- - --------|| + 2*I*im|atan|- - --------|| + 2*re|atan|- + --------|| + 2*I*im|atan|- + --------||
  2        \    \4      4    //         \    \4      4    //       \    \4      4    //         \    \4      4    //

\left(- \frac{\pi}{2} + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{4} - \frac{\sqrt{15} i}{4} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{4} - \frac{\sqrt{15} i}{4} \right)}\right)}\right)\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{4} + \frac{\sqrt{15} i}{4} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{4} + \frac{\sqrt{15} i}{4} \right)}\right)}\right)

    /    /        ____\\       /    /        ____\\              /    /        ____\\         /    /        ____\\
    |    |1   I*\/ 15 ||       |    |1   I*\/ 15 ||   pi         |    |1   I*\/ 15 ||         |    |1   I*\/ 15 ||
2*re|atan|- - --------|| + 2*re|atan|- + --------|| - -- + 2*I*im|atan|- - --------|| + 2*I*im|atan|- + --------||
    \    \4      4    //       \    \4      4    //   2          \    \4      4    //         \    \4      4    //

- \frac{\pi}{2} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{4} - \frac{\sqrt{15} i}{4} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{4} + \frac{\sqrt{15} i}{4} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{4} - \frac{\sqrt{15} i}{4} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{4} + \frac{\sqrt{15} i}{4} \right)}\right)}

producto

     /    /    /        ____\\         /    /        ____\\\ /    /    /        ____\\         /    /        ____\\\
-pi  |    |    |1   I*\/ 15 ||         |    |1   I*\/ 15 ||| |    |    |1   I*\/ 15 ||         |    |1   I*\/ 15 |||
----*|2*re|atan|- - --------|| + 2*I*im|atan|- - --------|||*|2*re|atan|- + --------|| + 2*I*im|atan|- + --------|||
 2   \    \    \4      4    //         \    \4      4    /// \    \    \4      4    //         \    \4      4    ///

- \frac{\pi}{2} \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{4} - \frac{\sqrt{15} i}{4} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{4} - \frac{\sqrt{15} i}{4} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{4} + \frac{\sqrt{15} i}{4} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{4} + \frac{\sqrt{15} i}{4} \right)}\right)}\right)

      /    /    /        ____\\     /    /        ____\\\ /    /    /        ____\\     /    /        ____\\\
      |    |    |1   I*\/ 15 ||     |    |1   I*\/ 15 ||| |    |    |1   I*\/ 15 ||     |    |1   I*\/ 15 |||
-2*pi*|I*im|atan|- - --------|| + re|atan|- - --------|||*|I*im|atan|- + --------|| + re|atan|- + --------|||
      \    \    \4      4    //     \    \4      4    /// \    \    \4      4    //     \    \4      4    ///

- 2 \pi \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{4} - \frac{\sqrt{15} i}{4} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{4} - \frac{\sqrt{15} i}{4} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{4} + \frac{\sqrt{15} i}{4} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{4} + \frac{\sqrt{15} i}{4} \right)}\right)}\right)

-2*pi*(i*im(atan(1/4 - i*sqrt(15)/4)) + re(atan(1/4 - i*sqrt(15)/4)))*(i*im(atan(1/4 + i*sqrt(15)/4)) + re(atan(1/4 + i*sqrt(15)/4)))

Respuesta rápida [src]

     -pi 
x1 = ----
      2

x_{1} = - \frac{\pi}{2}

         /    /        ____\\         /    /        ____\\
         |    |1   I*\/ 15 ||         |    |1   I*\/ 15 ||
x2 = 2*re|atan|- - --------|| + 2*I*im|atan|- - --------||
         \    \4      4    //         \    \4      4    //

x_{2} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{4} - \frac{\sqrt{15} i}{4} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{4} - \frac{\sqrt{15} i}{4} \right)}\right)}

         /    /        ____\\         /    /        ____\\
         |    |1   I*\/ 15 ||         |    |1   I*\/ 15 ||
x3 = 2*re|atan|- + --------|| + 2*I*im|atan|- + --------||
         \    \4      4    //         \    \4      4    //

x_{3} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{4} + \frac{\sqrt{15} i}{4} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{4} + \frac{\sqrt{15} i}{4} \right)}\right)}

x3 = 2*re(atan(1/4 + sqrt(15)*i/4)) + 2*i*im(atan(1/4 + sqrt(15)*i/4))

Respuesta numérica [src]

x1 = -45.5530933379328

x2 = -83.2522055607843

x3 = 98.9601682813222

x4 = -64.402649173144

x5 = -58.1194639983404

x6 = -20.4203520160774

x7 = -89.5353904664517

x8 = -51.8362786894957

x9 = -83.2522049833183

x10 = -76.9690196523847

x11 = -76.9690203364266

x12 = 67.5442422976148

x13 = -14.1371668379482

x14 = 92.676983594607

x15 = 4.71238875280883

x16 = 23.5619451408423

x17 = 23.5619445854305

x18 = -76.9690194223839

x19 = 80.110613139437

x20 = -32.9867229016282

x21 = 29.8451303220427

x22 = -39.2699084040555

x23 = -14.137166267618

x24 = 73.8274272534934

x25 = 92.6769830669358

x26 = 36.1283157093032

x27 = -64.4026497009475

x28 = 98.9601689505548

x29 = 42.4115009127929

x30 = -89.5353907488532

x31 = -32.9867225012491

x32 = 48.6946864510303

x33 = -45.5530935900185

x34 = 61.2610570733106

x35 = -32.9867229219624

x36 = -158.650429510901

x37 = 61.2610563902501

x38 = 54.9778711266118

x39 = -95.8185758680815

x40 = -20.4203525581159

x41 = 2122.14583792168

x42 = 17.2787599191456

x43 = -32.9867231822668

x44 = -70.6858343897312

x45 = -26.7035379113368

x46 = -39.2699078379722

x47 = -227.765467380722

x48 = -14.1371669906886

x49 = 48.6946859098066

x50 = -58.119464108743

x51 = -51.8362794146821

x52 = 10.9955739720808

x53 = 42.411500728142

x54 = -7.85398149740641

x55 = -1.57079621145266

x56 = -70.6858350616861

x57 = 17.2787592393122

x58 = 54.9778718002295

x59 = 4.71238930682327

x60 = -83.2522056059716

x61 = 10.9955746496251

x62 = 73.8274274816964

x63 = 67.5442417296428

x64 = -95.8185764895439

x65 = -114.668132439338

x66 = -26.7035372352027

x67 = -7.85398233977009

x68 = 86.3937978874973

x69 = -1.57079643102431

x70 = 29.8451301301352

x71 = 86.3937980345907

x71 = 86.3937980345907

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

2sin^2x+cos^2x-3sinx-5=0 la ecuación

Solución numérica:

Solución