Sr Examen

Lang:

-sin(x)-sqrt(2)/2=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Ha introducido [src]

            ___    
          \/ 2     
-sin(x) - ----- = 0
            2

- \sin{\left(x \right)} - \frac{\sqrt{2}}{2} = 0

Simplificar

Solución detallada

Tenemos la ecuación

- \sin{\left(x \right)} - \frac{\sqrt{2}}{2} = 0

es la ecuación trigonométrica más simple

Transportemos -sqrt(2)/2 al miembro derecho de la ecuación

cambiando el signo de -sqrt(2)/2

Obtenemos:

- \sin{\left(x \right)} - \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2} = \frac{\sqrt{2}}{2}

Dividamos ambos miembros de la ecuación en -1

La ecuación se convierte en

\sin{\left(x \right)} = - \frac{\sqrt{2}}{2}

Esta ecuación se reorganiza en

x = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)}

x = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)} + \pi

x = 2 \pi n - \frac{\pi}{4}

x = 2 \pi n + \frac{5 \pi}{4}

, donde n es cualquier número entero

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

     -pi 
x1 = ----
      4

x_{1} = - \frac{\pi}{4}

     5*pi
x2 = ----
      4

x_{2} = \frac{5 \pi}{4}

x2 = 5*pi/4

Suma y producto de raíces [src]

suma

  pi   5*pi
- -- + ----
  4     4

- \frac{\pi}{4} + \frac{5 \pi}{4}

pi

\pi

producto

-pi  5*pi
----*----
 4    4

- \frac{\pi}{4} \frac{5 \pi}{4}

     2
-5*pi 
------
  16

- \frac{5 \pi^{2}}{16}

-5*pi^2/16

Respuesta numérica [src]

x1 = -704.502152567511

x2 = -52.621676947629

x3 = -33.7721210260903

x4 = -101.316363078271

x5 = 93.4623814442964

x6 = 60.4756585816035

x7 = 43.1968989868597

x8 = -830.165858711103

x9 = -96.6039740978861

x10 = -19.6349540849362

x11 = -44.7676953136546

x12 = 11.7809724509617

x13 = -371.493331286993

x14 = 18.0641577581413

x15 = 66.7588438887831

x16 = -2865.91789823729

x17 = -71.4712328691678

x18 = 74.6128255227576

x19 = 41.6261026600648

x20 = -215482.625507887

x21 = -57.3340659280137

x22 = -8.63937979737193

x23 = -76.1836218495525

x24 = -32.2013246992954

x25 = -58.9048622548086

x26 = 30.6305283725005

x27 = -82.4668071567321

x28 = -38.484510006475

x29 = 3.92699081698724

x30 = 73.0420291959627

x31 = -14.9225651045515

x32 = -77.7544181763474

x33 = 22.776546738526

x34 = 79.3252145031423

x35 = 68.329640215578

x36 = 16.4933614313464

x37 = 10.2101761241668

x38 = -88.7499924639117

x39 = 85.6083998103219

x40 = 80.8960108299372

x41 = -51.0508806208341

x42 = -21.2057504117311

x43 = -2.35619449019234

x44 = 35.3429173528852

x45 = 652.665873783279

x46 = 98.174770424681

x47 = -90.3207887907066

x48 = 36.9137136796801

x49 = -46.3384916404494

x50 = -69.9004365423729

x51 = -7.06858347057703

x52 = -27.4889357189107

x53 = 49.4800842940392

x54 = 62.0464549083984

x55 = -25.9181393921158

x56 = -0.785398163397448

x57 = 24.3473430653209

x58 = -84.037603483527

x59 = 5.49778714378214

x60 = -40.0553063332699

x61 = -65.1880475619882

x62 = -63.6172512351933

x63 = 47.9092879672443

x64 = 99.7455667514759

x65 = -128.019900633784

x66 = 54.1924732744239

x67 = 55.7632696012188

x68 = -95.0331777710912

x69 = 29.0597320457056

x70 = 91.8915851175014

x71 = -13.3517687777566

x72 = 87.1791961371168

x72 = 87.1791961371168