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sqrt3*sin4x+cos4x=0 la ecuación

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Ha introducido [src]

  ___                        
\/ 3 *sin(4*x) + cos(4*x) = 0

\sqrt{3} \sin{\left(4 x \right)} + \cos{\left(4 x \right)} = 0

Simplificar

Solución detallada

Tenemos la ecuación

\sqrt{3} \sin{\left(4 x \right)} + \cos{\left(4 x \right)} = 0

cambiamos:

\frac{\sqrt{3} \sin{\left(4 x \right)}}{\cos{\left(4 x \right)}} = -1

\sqrt{3} \tan{\left(4 x \right)} = -1

es la ecuación trigonométrica más simple

Dividamos ambos miembros de la ecuación en sqrt(3)

La ecuación se convierte en

\tan{\left(4 x \right)} = \frac{\sqrt{3}}{3}

Esta ecuación se reorganiza en

4 x = \pi n + \operatorname{atan}{\left(\frac{\sqrt{3}}{3} \right)}

4 x = \pi n + \frac{\pi}{6}

, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en

4

obtenemos la respuesta:

x_{1} = \frac{\pi n}{4} + \frac{\pi}{24}

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

     -pi 
x1 = ----
      24

x_{1} = - \frac{\pi}{24}

x1 = -pi/24

Suma y producto de raíces [src]

suma

-pi 
----
 24

- \frac{\pi}{24}

-pi 
----
 24

- \frac{\pi}{24}

producto

-pi 
----
 24

- \frac{\pi}{24}

-pi 
----
 24

- \frac{\pi}{24}

-pi/24

Respuesta numérica [src]

x1 = -77.885317870247

x2 = -52.7525766415286

x3 = 2.22529479629277

x4 = 32.8558231687933

x5 = -93.5932811381959

x6 = -23.692844595823

x7 = -67.6751417460801

x8 = -19.7658537788358

x9 = -57.4649656219133

x10 = 24.2164433714213

x11 = 17.9332580642417

x12 = 79.9797129726402

x13 = -18.1950574520409

x14 = -40.1862060271694

x15 = 56.4177680707167

x16 = -99.8764664453755

x17 = 82.3359074628325

x18 = 16.3624617374468

x19 = 53.2761754171269

x20 = 43.8513974563575

x21 = -15.8388629618485

x22 = -89.6662903212087

x23 = 46.2075919465499

x24 = 20.2894525544341

x25 = -26.0490390860154

x26 = -45.6839931709516

x27 = -33.9030207199899

x28 = 90.189889096807

x29 = 83.9067037896274

x30 = -70.0313362362725

x31 = 50.1345827635371

x32 = -71.6021325630674

x33 = -85.7392995042214

x34 = 87.8336946066146

x35 = -84.1685031774265

x36 = 86.2628982798197

x37 = -63.7481509290929

x38 = 68.1987405216784

x39 = 21.860248881229

x40 = -11.9118721448613

x41 = 99.6146670575764

x42 = -44.1131968441567

x43 = 6.15228561328001

x44 = -55.8941692951184

x45 = -73.9583270532597

x46 = 42.2806011295626

x47 = -27.6198354128103

x48 = 61.9155552144988

x49 = -7.98488132787406

x50 = -92.022484811401

x51 = -22.1220482690281

x52 = -88.0954939944138

x53 = -41.7570023539643

x54 = 94.1168799137942

x55 = 64.2717497046912

x56 = -29.9760299030026

x57 = -49.6109839879388

x58 = 57.9885643975116

x59 = 76.0527221556529

x60 = -1.70169602069447

x61 = -48.0401876611439

x62 = 65.8425460314861

x63 = 98.0438707307815

x64 = -51.9671784781312

x65 = -81.8123086872342

x66 = 25.0018415348188

x67 = 100.400065220974

x68 = -66.1043454192852

x69 = -95.9494756283883

x70 = -4.05789051088682

x71 = -5.62868683768171

x72 = 54.0615735805244

x73 = -81.0269105238367

x74 = 72.1257313386657

x75 = -9.55567765466895

x76 = 35.997415822383

x77 = 14.0062672472545

x78 = -37.8300115369771

x79 = -59.8211601121056

x80 = 60.3447588877039

x81 = 3.79609112308767

x82 = -62.177354602298

x83 = 38.3536103125754

x84 = 10.0792764302673

x85 = 32.0704250053958

x86 = 78.4089166458453

x87 = -40.9716041905669

x88 = 28.1434341884086

x89 = -0.130899693899575

x90 = 39.9244066393703

x91 = 34.4266194955881

x92 = 12.4354709204596

x92 = 12.4354709204596