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4*cosx^2*sinx+cosx=0
Expresiones con funciones
sinx
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4cosx^2sinx-cosx=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

     2                       
4*cos (x)*sin(x) - cos(x) = 0

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

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

     -pi 
x1 = ----
      2

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

     pi
x2 = --
     2

$$x_{2} = \frac{\pi}{2}$$

           /                  ___________\
           |       ___       /       ___ |
x3 = 2*atan\-2 + \/ 3  + 2*\/  2 - \/ 3  /

$$x_{3} = 2 \operatorname{atan}{\left(-2 + 2 \sqrt{2 - \sqrt{3}} + \sqrt{3} \right)}$$

            /                 ___________\
            |      ___       /       ___ |
x4 = -2*atan\2 - \/ 3  + 2*\/  2 - \/ 3  /

$$x_{4} = - 2 \operatorname{atan}{\left(- \sqrt{3} + 2 \sqrt{2 - \sqrt{3}} + 2 \right)}$$

            /                 ___________\
            |      ___       /       ___ |
x5 = -2*atan\2 + \/ 3  + 2*\/  2 + \/ 3  /

$$x_{5} = - 2 \operatorname{atan}{\left(\sqrt{3} + 2 + 2 \sqrt{\sqrt{3} + 2} \right)}$$

            /                 ___________\
            |      ___       /       ___ |
x6 = -2*atan\2 + \/ 3  - 2*\/  2 + \/ 3  /

$$x_{6} = - 2 \operatorname{atan}{\left(- 2 \sqrt{\sqrt{3} + 2} + \sqrt{3} + 2 \right)}$$

x6 = -2*atan(-2*sqrt(sqrt(3) + 2) + sqrt(3) + 2)

Suma y producto de raíces [src]

suma

                  /                  ___________\         /                 ___________\         /                 ___________\         /                 ___________\
  pi   pi         |       ___       /       ___ |         |      ___       /       ___ |         |      ___       /       ___ |         |      ___       /       ___ |
- -- + -- + 2*atan\-2 + \/ 3  + 2*\/  2 - \/ 3  / - 2*atan\2 - \/ 3  + 2*\/  2 - \/ 3  / - 2*atan\2 + \/ 3  + 2*\/  2 + \/ 3  / - 2*atan\2 + \/ 3  - 2*\/  2 + \/ 3  /
  2    2

$$\left(- 2 \operatorname{atan}{\left(\sqrt{3} + 2 + 2 \sqrt{\sqrt{3} + 2} \right)} + \left(- 2 \operatorname{atan}{\left(- \sqrt{3} + 2 \sqrt{2 - \sqrt{3}} + 2 \right)} + \left(\left(- \frac{\pi}{2} + \frac{\pi}{2}\right) + 2 \operatorname{atan}{\left(-2 + 2 \sqrt{2 - \sqrt{3}} + \sqrt{3} \right)}\right)\right)\right) - 2 \operatorname{atan}{\left(- 2 \sqrt{\sqrt{3} + 2} + \sqrt{3} + 2 \right)}$$

        /                 ___________\         /                 ___________\         /                 ___________\         /                  ___________\
        |      ___       /       ___ |         |      ___       /       ___ |         |      ___       /       ___ |         |       ___       /       ___ |
- 2*atan\2 + \/ 3  - 2*\/  2 + \/ 3  / - 2*atan\2 + \/ 3  + 2*\/  2 + \/ 3  / - 2*atan\2 - \/ 3  + 2*\/  2 - \/ 3  / + 2*atan\-2 + \/ 3  + 2*\/  2 - \/ 3  /

$$- 2 \operatorname{atan}{\left(\sqrt{3} + 2 + 2 \sqrt{\sqrt{3} + 2} \right)} - 2 \operatorname{atan}{\left(- \sqrt{3} + 2 \sqrt{2 - \sqrt{3}} + 2 \right)} - 2 \operatorname{atan}{\left(- 2 \sqrt{\sqrt{3} + 2} + \sqrt{3} + 2 \right)} + 2 \operatorname{atan}{\left(-2 + 2 \sqrt{2 - \sqrt{3}} + \sqrt{3} \right)}$$

producto

              /                  ___________\        /                 ___________\        /                 ___________\        /                 ___________\
-pi  pi       |       ___       /       ___ |        |      ___       /       ___ |        |      ___       /       ___ |        |      ___       /       ___ |
----*--*2*atan\-2 + \/ 3  + 2*\/  2 - \/ 3  /*-2*atan\2 - \/ 3  + 2*\/  2 - \/ 3  /*-2*atan\2 + \/ 3  + 2*\/  2 + \/ 3  /*-2*atan\2 + \/ 3  - 2*\/  2 + \/ 3  /
 2   2

$$- \frac{\pi}{2} \frac{\pi}{2} \cdot 2 \operatorname{atan}{\left(-2 + 2 \sqrt{2 - \sqrt{3}} + \sqrt{3} \right)} \left(- 2 \operatorname{atan}{\left(- \sqrt{3} + 2 \sqrt{2 - \sqrt{3}} + 2 \right)}\right) \left(- 2 \operatorname{atan}{\left(\sqrt{3} + 2 + 2 \sqrt{\sqrt{3} + 2} \right)}\right) \left(- 2 \operatorname{atan}{\left(- 2 \sqrt{\sqrt{3} + 2} + \sqrt{3} + 2 \right)}\right)$$

          /                  ___________\     /                 ___________\     /                 ___________\     /                 ___________\
    2     |       ___       /       ___ |     |      ___       /       ___ |     |      ___       /       ___ |     |      ___       /       ___ |
4*pi *atan\-2 + \/ 3  + 2*\/  2 - \/ 3  /*atan\2 + \/ 3  - 2*\/  2 + \/ 3  /*atan\2 + \/ 3  + 2*\/  2 + \/ 3  /*atan\2 - \/ 3  + 2*\/  2 - \/ 3  /

$$4 \pi^{2} \operatorname{atan}{\left(-2 + 2 \sqrt{2 - \sqrt{3}} + \sqrt{3} \right)} \operatorname{atan}{\left(- \sqrt{3} + 2 \sqrt{2 - \sqrt{3}} + 2 \right)} \operatorname{atan}{\left(\sqrt{3} + 2 + 2 \sqrt{\sqrt{3} + 2} \right)} \operatorname{atan}{\left(- 2 \sqrt{\sqrt{3} + 2} + \sqrt{3} + 2 \right)}$$

4*pi^2*atan(-2 + sqrt(3) + 2*sqrt(2 - sqrt(3)))*atan(2 + sqrt(3) - 2*sqrt(2 + sqrt(3)))*atan(2 + sqrt(3) + 2*sqrt(2 + sqrt(3)))*atan(2 - sqrt(3) + 2*sqrt(2 - sqrt(3)))

Respuesta numérica [src]

x1 = 97.6511716490827

x2 = -7.85398163397448

x3 = 1.5707963267949

x4 = -64.4026493985908

x5 = -1.83259571459405

x6 = -58.1194640914112

x7 = -20.4203522483337

x8 = 0.261799387799149

x9 = -45.553093477052

x10 = -29.845130209103

x11 = 15.9697626557481

x12 = -74.0892267471593

x13 = -61.261056745001

x14 = -102.363560629467

x15 = -52.0980781720307

x16 = 72.5184304203644

x17 = 95.8185759344887

x18 = -67.8060414399797

x19 = 81.9432083811338

x20 = 58.1194640914112

x21 = 32.7249234748937

x22 = -73.8274273593601

x23 = 7.85398163397448

x24 = 6.54498469497874

x25 = 44.2440965380563

x26 = 4.45058959258554

x27 = -83.5140047079287

x28 = 50.5272818452358

x29 = -81.4196096055355

x30 = 88.2263936883134

x31 = 89.5353906273091

x32 = 23.5619449019235

x33 = -17.540558982543

x34 = 26.4417381677141

x35 = -48.9564855184409

x36 = -80.3724120543389

x37 = -59.4284610304069

x38 = 42.1497014356631

x39 = 28.5361332701073

x40 = -42.4115008234622

x41 = 94.5095789954929

x42 = 101.839961853869

x43 = -26.9653369433124

x44 = 79.8488132787406

x45 = -65.7116463375865

x46 = 39.2699081698724

x47 = 17.0169602069447

x48 = -14.1371669411541

x49 = 59.9520598060052

x50 = 20.1585528605345

x51 = 29.845130209103

x52 = -28.012534494509

x53 = -23.8237442897226

x54 = -86.3937979737193

x55 = 80.1106126665397

x56 = 35.8665161284835

x57 = -4.97418836818384

x58 = 56.8104671524154

x59 = -95.8185759344887

x60 = -36.1283155162826

x61 = 51.8362787842316

x62 = -21.7293491873294

x63 = -89.7971900151083

x64 = -87.7027949127151

x65 = -71.9948316447661

x66 = 57.857664703612

x67 = -15.4461638801498

x68 = -61.5228561328001

x69 = -39.5317075576716

x70 = 37.9609112308767

x71 = 45.553093477052

x72 = -43.720497762458

x73 = -45.8148928648512

x74 = 48.4328867428426

x75 = -51.8362787842316

x76 = -96.0803753222878

x77 = -6.02138591938044

x78 = 36.1283155162826

x79 = -92.9387826686981

x80 = 66.2352451131848

x81 = -37.4373124552784

x82 = 86.1319985859202

x83 = -50.0036830696375

x84 = 73.8274273593601

x85 = 14.1371669411541

x86 = -70.9476340935695

x87 = 64.1408500107916

x88 = 22.2529479629277

x89 = 70.4240353179712

x90 = -80.1106126665397

x91 = 92.4151838930998

x92 = -93.9859802198946

x93 = 67.5442420521806

x93 = 67.5442420521806

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Solución numérica:

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