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cos(6*x)-sin(x)=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

cos(6*x) - sin(x) = 0

$$- \sin{\left(x \right)} + \cos{\left(6 x \right)} = 0$$

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 = ----
      10

$$x_{2} = - \frac{\pi}{10}$$

     pi
x3 = --
     14

$$x_{3} = \frac{\pi}{14}$$

     13*pi
x4 = -----
       14

$$x_{4} = \frac{13 \pi}{14}$$

           /     3/14\
x5 = -I*log\-(-1)    /

$$x_{5} = - i \log{\left(- \left(-1\right)^{\frac{3}{14}} \right)}$$

                                              /   /pi\\
            /    _____________________\       |cos|--||
            |   /    2/pi\      2/pi\ |       |   \7 /|
x6 = - I*log|  /  cos |--| + sin |--| | + atan|-------|
            \\/       \7 /       \7 / /       |   /pi\|
                                              |sin|--||
                                              \   \7 //

$$x_{6} = - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{7} \right)}} \right)}$$

           /   /2*pi\\                                       
           |cos|----||        /    _________________________\
           |   \ 7  /|        |   /    2/2*pi\      2/2*pi\ |
x7 = - atan|---------| - I*log|  /  cos |----| + sin |----| |
           |   /2*pi\|        \\/       \ 7  /       \ 7  / /
           |sin|----||                                       
           \   \ 7  //

$$x_{7} = - \operatorname{atan}{\left(\frac{\cos{\left(\frac{2 \pi}{7} \right)}}{\sin{\left(\frac{2 \pi}{7} \right)}} \right)} - i \log{\left(\sqrt{\cos^{2}{\left(\frac{2 \pi}{7} \right)} + \sin^{2}{\left(\frac{2 \pi}{7} \right)}} \right)}$$

              /         2/pi\\                                                      
              |1 - 2*sin |--||        /    ________________________________________\
              |          \14/|        |   /        2/pi\        2/pi\        4/pi\ |
x8 = pi - atan|--------------| - I*log|  /  1 + sin |--| - 4*sin |--| + 4*sin |--| |
              |      /pi\    |        \\/           \7 /         \14/         \14/ /
              |   sin|--|    |                                                      
              \      \7 /    /

$$x_{8} = - \operatorname{atan}{\left(\frac{1 - 2 \sin^{2}{\left(\frac{\pi}{14} \right)}}{\sin{\left(\frac{\pi}{7} \right)}} \right)} - i \log{\left(\sqrt{- 4 \sin^{2}{\left(\frac{\pi}{14} \right)} + 4 \sin^{4}{\left(\frac{\pi}{14} \right)} + \sin^{2}{\left(\frac{\pi}{7} \right)} + 1} \right)} + \pi$$

           /             ___________                       ___________\
           |      ___   /       ___        ___     ____   /       ___ |
           |I   \/ 2 *\/  5 + \/ 5     I*\/ 5    \/ 10 *\/  5 + \/ 5  |
x9 = -I*log|- - -------------------- + ------- + ---------------------|
           \4            8                4                8          /

$$x_{9} = - i \log{\left(- \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{8} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{8} + \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)}$$

            /                       ___________             ___________             ___________            ___________\
            |        ___     ___   /       ___      ____   /       ___      ____   /       ___      ___   /       ___ |
            |I   I*\/ 5    \/ 2 *\/  5 + \/ 5     \/ 10 *\/  5 + \/ 5     \/ 10 *\/  5 - \/ 5     \/ 2 *\/  5 - \/ 5  |
x10 = -I*log|- - ------- - -------------------- - --------------------- - --------------------- + --------------------|
            \4      4               16                      16                      16                     16         /

$$x_{10} = - i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{5} i}{4} + \frac{i}{4} \right)}$$

            /             ___________            ___________             ___________                       ___________\
            |      ___   /       ___      ___   /       ___      ____   /       ___        ___     ____   /       ___ |
            |I   \/ 2 *\/  5 + \/ 5     \/ 2 *\/  5 - \/ 5     \/ 10 *\/  5 + \/ 5     I*\/ 5    \/ 10 *\/  5 - \/ 5  |
x11 = -I*log|- - -------------------- - -------------------- - --------------------- + ------- + ---------------------|
            \4            16                     16                      16               4                16         /

$$x_{11} = - i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} + \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)}$$

x11 = -i*log(-sqrt(10)*sqrt(sqrt(5) + 5)/16 - sqrt(2)*sqrt(sqrt(5) + 5)/16 - sqrt(2)*sqrt(5 - sqrt(5))/16 + sqrt(10)*sqrt(5 - sqrt(5))/16 + i/4 + sqrt(5)*i/4)

Respuesta numérica [src]

x1 = -69.7882368047447

x2 = 73.8274274336363

x3 = -51.8362786949167

x4 = 86.3937979061014

x5 = -35.6795165657698

x6 = 3.45575191894877

x7 = 60.0044196835651

x8 = 70.2370357552575

x9 = 68.8008791136165

x10 = 78.3154168644884

x11 = -75.712382951514

x12 = 96.2673748850015

x13 = 44.2066966255135

x14 = 42.4115007536779

x15 = 5.96902604182061

x16 = -24.0107438524363

x17 = -95.8185758690789

x18 = -87.7401948252578

x19 = 54.0802735367957

x20 = 98.0625706870528

x21 = -7.85398152538593

x22 = 8.30278058448731

x23 = -31.7300858012569

x24 = -43.7578976750007

x25 = -77.8666179139756

x26 = -17.7275585452567

x27 = 18.1763574957695

x28 = -58.1194640200244

x29 = -97.61377173654

x30 = -62.6074535965395

x31 = -48.0663675999238

x32 = -92.0486647501809

x33 = -85.7654794430014

x34 = -1.57079639656738

x35 = 39.8982267005904

x36 = 81.905808468591

x37 = 0.224399475256414

x38 = 63.9538504480779

x39 = 38.8211092193596

x40 = 34.3331197142313

x41 = -55.6061899685393

x42 = 76.340701482232

x43 = 82.8034063696167

x44 = -81.9955682586936

x45 = 83.8805238508475

x46 = -38.0132711084365

x47 = -61.7098556955138

x48 = 20.8691511988465

x49 = -15.9323627432054

x50 = 22.3053078404875

x51 = -21.6769893097696

x52 = -89.5353906870099

x53 = -27.9601746169492

x54 = -45.5530935438943

x55 = 46.0018924275648

x56 = -6.05878583192317

x57 = -4.08407044966673

x58 = -40.1675060708981

x59 = -79.6618137160269

x60 = 93.9336203423348

x61 = -78.2256570743859

x62 = 88.1889937757706

x63 = -31.1915270606415

x64 = -99.5884871187965

x65 = 72.0322315573088

x66 = 47.4380490692059

x67 = 32.3584043319749

x68 = -43.0398193541802

x69 = 19.9715532978208

x70 = 28.0499344070517

x71 = 29.8451302843512

x72 = -14.13716686694

x73 = 26.2547386050004

x74 = -25.8059396544876

x75 = -67.9930410026934

x76 = 91.420346219463

x77 = 37.9235113183339

x78 = -53.6314745862829

x79 = -18.6251564462823

x80 = -33.8843207637185

x81 = 52.2850777347444

x82 = 10.0979763865386

x83 = -59.9146598934625

x84 = 62.1586546460266

x85 = -71.9424717672063

x86 = 12.2522113490002

x87 = -84.1498032211552

x88 = 26.0752190247953

x89 = -65.6592864600267

x90 = -11.6238928182822

x91 = -94.0233801324374

x92 = 66.2876049907446

x93 = 49.9513231920777

x94 = 100.216805649514

x95 = 89.9841895778219

x96 = 16.0221225333079

x97 = 56.2345084992573

x98 = -50.0410829821803

x99 = -9.64917743602579

x99 = -9.64917743602579

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Expresiones con funciones

cos(6*x)-sin(x)=0 la ecuación

Solución numérica:

Solución