Sr Examen

Otras calculadoras

sec(3*x)-6*cos(3*x)=4*sin(3*x) la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

v

Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
sec(3*x) - 6*cos(3*x) = 4*sin(3*x)
$$- 6 \cos{\left(3 x \right)} + \sec{\left(3 x \right)} = 4 \sin{\left(3 x \right)}$$
Gráfica
Suma y producto de raíces [src]
suma
                  /      ____\         /      ____\
                  |1   \/ 26 |         |1   \/ 26 |
            2*atan|- - ------|   2*atan|- + ------|
  pi   pi         \5     5   /         \5     5   /
- -- + -- - ------------------ - ------------------
  12   4            3                    3         
$$- \frac{2 \operatorname{atan}{\left(\frac{1}{5} + \frac{\sqrt{26}}{5} \right)}}{3} + \left(- \frac{2 \operatorname{atan}{\left(\frac{1}{5} - \frac{\sqrt{26}}{5} \right)}}{3} + \left(- \frac{\pi}{12} + \frac{\pi}{4}\right)\right)$$
=
        /      ____\         /      ____\     
        |1   \/ 26 |         |1   \/ 26 |     
  2*atan|- - ------|   2*atan|- + ------|     
        \5     5   /         \5     5   /   pi
- ------------------ - ------------------ + --
          3                    3            6 
$$- \frac{2 \operatorname{atan}{\left(\frac{1}{5} + \frac{\sqrt{26}}{5} \right)}}{3} - \frac{2 \operatorname{atan}{\left(\frac{1}{5} - \frac{\sqrt{26}}{5} \right)}}{3} + \frac{\pi}{6}$$
producto
               /      ____\        /      ____\
               |1   \/ 26 |        |1   \/ 26 |
        -2*atan|- - ------| -2*atan|- + ------|
-pi  pi        \5     5   /        \5     5   /
----*--*-------------------*-------------------
 12  4           3                   3         
$$- \frac{\pi}{12} \frac{\pi}{4} \left(- \frac{2 \operatorname{atan}{\left(\frac{1}{5} - \frac{\sqrt{26}}{5} \right)}}{3}\right) \left(- \frac{2 \operatorname{atan}{\left(\frac{1}{5} + \frac{\sqrt{26}}{5} \right)}}{3}\right)$$
=
         /      ____\     /      ____\ 
   2     |1   \/ 26 |     |1   \/ 26 | 
-pi *atan|- - ------|*atan|- + ------| 
         \5     5   /     \5     5   / 
---------------------------------------
                  108                  
$$- \frac{\pi^{2} \operatorname{atan}{\left(\frac{1}{5} - \frac{\sqrt{26}}{5} \right)} \operatorname{atan}{\left(\frac{1}{5} + \frac{\sqrt{26}}{5} \right)}}{108}$$
-pi^2*atan(1/5 - sqrt(26)/5)*atan(1/5 + sqrt(26)/5)/108
Respuesta rápida [src]
     -pi 
x1 = ----
      12 
$$x_{1} = - \frac{\pi}{12}$$
     pi
x2 = --
     4 
$$x_{2} = \frac{\pi}{4}$$
            /      ____\
            |1   \/ 26 |
     -2*atan|- - ------|
            \5     5   /
x3 = -------------------
              3         
$$x_{3} = - \frac{2 \operatorname{atan}{\left(\frac{1}{5} - \frac{\sqrt{26}}{5} \right)}}{3}$$
            /      ____\
            |1   \/ 26 |
     -2*atan|- + ------|
            \5     5   /
x4 = -------------------
              3         
$$x_{4} = - \frac{2 \operatorname{atan}{\left(\frac{1}{5} + \frac{\sqrt{26}}{5} \right)}}{3}$$
x4 = -2*atan(1/5 + sqrt(26)/5)/3
Respuesta numérica [src]
x1 = 40.2513072011191
x2 = 20.6821516361328
x3 = -74.6128255227576
x4 = -33.7721210260903
x5 = 3.92699081698724
x6 = 12.30457122656
x7 = 81.4196096055355
x8 = -81.9432083811338
x9 = -31.6777259236971
x10 = -99.7455667514759
x11 = 8.11578102177363
x12 = 84.2336043513762
x13 = 62.2424557762476
x14 = -2.35619449019234
x15 = -55.7632696012188
x16 = 32.2013246992954
x17 = -75.6600230739542
x18 = 78.2780169519457
x19 = 37.1097145475293
x20 = -66.2352451131848
x21 = 57.3340659280137
x22 = 79.3252145031423
x23 = 91.8915851175014
x24 = 1.83259571459405
x25 = 6.02138591938044
x26 = 93.9859802198946
x27 = -15.9697626557481
x28 = -42.1497014356631
x29 = -25.7221385242666
x30 = -97.6511716490827
x31 = 52.0980781720307
x32 = -79.8488132787406
x33 = 13.3517687777566
x34 = 42.6733002112614
x35 = 47.9092879672443
x36 = 18.2601586259905
x37 = -11.7809724509617
x38 = 100.269165527074
x39 = -62.0464549083984
x40 = -57.857664703612
x41 = -47.3856891916461
x42 = -18.0641577581413
x43 = 46.5344925082986
x44 = 5310.07698273015
x45 = 54.1924732744239
x46 = -50.5272818452358
x47 = -85.0848010347236
x48 = -77.7544181763474
x49 = -312.326669644385
x50 = -88.2263936883134
x51 = 35.3429173528852
x52 = 23.8237442897226
x53 = 34.2957198016886
x54 = -59.9520598060052
x55 = 91.5639872097523
x56 = 71.9948316447661
x57 = 163.10101859887
x58 = -93.7899793520455
x59 = -37.9609112308767
x60 = -8.63937979737193
x61 = -86.1319985859202
x62 = 76.1836218495525
x63 = 69.9004365423729
x64 = -44.2440965380563
x65 = 98.174770424681
x66 = 41.6261026600648
x67 = -20.1585528605345
x68 = 64.6644487863899
x69 = 96.0803753222878
x70 = -35.8665161284835
x71 = -27.4889357189107
x72 = -52.621676947629
x73 = 56.2868683768171
x74 = -30.6305283725005
x75 = -1.30899693899575
x76 = 283.20113907873
x77 = 74.0892267471593
x78 = 59.4284610304069
x79 = -84.037603483527
x80 = 10.2101761241668
x81 = -9.68657734856853
x82 = 25.9181393921158
x83 = -72.5184304203644
x84 = 50.0036830696375
x85 = -3.73098994913805
x86 = 28.012534494509
x87 = 86.6555973615185
x88 = -40.0553063332699
x89 = 30.1069295969022
x90 = 67.4784435322306
x91 = -64.1408500107916
x92 = -13.8753675533549
x93 = -23.3001455141243
x94 = -5.49778714378214
x95 = -92.4151838930998
x95 = -92.4151838930998