Sr Examen

Otras calculadoras

2sin^2x+3sinxcosx-5cos^2x=0 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]
     2                             2       
2*sin (x) + 3*sin(x)*cos(x) - 5*cos (x) = 0
$$\left(2 \sin^{2}{\left(x \right)} + 3 \sin{\left(x \right)} \cos{\left(x \right)}\right) - 5 \cos^{2}{\left(x \right)} = 0$$
Gráfica
Respuesta rápida [src]
     -3*pi
x1 = -----
       4  
$$x_{1} = - \frac{3 \pi}{4}$$
     pi
x2 = --
     4 
$$x_{2} = \frac{\pi}{4}$$
           /      ____\
           |2   \/ 29 |
x3 = 2*atan|- - ------|
           \5     5   /
$$x_{3} = 2 \operatorname{atan}{\left(\frac{2}{5} - \frac{\sqrt{29}}{5} \right)}$$
           /      ____\
           |2   \/ 29 |
x4 = 2*atan|- + ------|
           \5     5   /
$$x_{4} = 2 \operatorname{atan}{\left(\frac{2}{5} + \frac{\sqrt{29}}{5} \right)}$$
x4 = 2*atan(2/5 + sqrt(29)/5)
Suma y producto de raíces [src]
suma
                    /      ____\         /      ____\
  3*pi   pi         |2   \/ 29 |         |2   \/ 29 |
- ---- + -- + 2*atan|- - ------| + 2*atan|- + ------|
   4     4          \5     5   /         \5     5   /
$$\left(\left(- \frac{3 \pi}{4} + \frac{\pi}{4}\right) + 2 \operatorname{atan}{\left(\frac{2}{5} - \frac{\sqrt{29}}{5} \right)}\right) + 2 \operatorname{atan}{\left(\frac{2}{5} + \frac{\sqrt{29}}{5} \right)}$$
=
      /      ____\         /      ____\     
      |2   \/ 29 |         |2   \/ 29 |   pi
2*atan|- - ------| + 2*atan|- + ------| - --
      \5     5   /         \5     5   /   2 
$$- \frac{\pi}{2} + 2 \operatorname{atan}{\left(\frac{2}{5} - \frac{\sqrt{29}}{5} \right)} + 2 \operatorname{atan}{\left(\frac{2}{5} + \frac{\sqrt{29}}{5} \right)}$$
producto
               /      ____\       /      ____\
-3*pi pi       |2   \/ 29 |       |2   \/ 29 |
-----*--*2*atan|- - ------|*2*atan|- + ------|
  4   4        \5     5   /       \5     5   /
$$- \frac{3 \pi}{4} \frac{\pi}{4} \cdot 2 \operatorname{atan}{\left(\frac{2}{5} - \frac{\sqrt{29}}{5} \right)} 2 \operatorname{atan}{\left(\frac{2}{5} + \frac{\sqrt{29}}{5} \right)}$$
=
           /      ____\     /      ____\
     2     |2   \/ 29 |     |2   \/ 29 |
-3*pi *atan|- - ------|*atan|- + ------|
           \5     5   /     \5     5   /
----------------------------------------
                   4                    
$$- \frac{3 \pi^{2} \operatorname{atan}{\left(\frac{2}{5} - \frac{\sqrt{29}}{5} \right)} \operatorname{atan}{\left(\frac{2}{5} + \frac{\sqrt{29}}{5} \right)}}{4}$$
-3*pi^2*atan(2/5 - sqrt(29)/5)*atan(2/5 + sqrt(29)/5)/4
Respuesta numérica [src]
x1 = -73.4469209822478
x2 = 23.9424512790358
x3 = 32.2013246992954
x4 = 66.7588438887831
x5 = -27.4889357189107
x6 = 10.2101761241668
x7 = -51.4557724071192
x8 = 61.6415631221133
x9 = -57.7389577142988
x10 = 44.7676953136546
x11 = -21.2057504117311
x12 = 45.9335998541644
x13 = 36.508821893395
x14 = 55.3583778149337
x15 = 89.9158970044215
x16 = 74.2079337364725
x17 = 8.23448801108685
x18 = 82.4668071567321
x19 = 67.9247484292929
x20 = -54.597365060709
x21 = -77.7544181763474
x22 = 88.7499924639117
x23 = 16.4933614313464
x24 = 41.6261026600648
x25 = 0.785398163397448
x26 = -46.3384916404494
x27 = -5.49778714378214
x28 = -84.037603483527
x29 = 91.8915851175014
x30 = -55.7632696012188
x31 = -71.4712328691678
x32 = -305.924777347892
x33 = -29.4646238319907
x34 = -65.1880475619882
x35 = 60.4756585816035
x36 = 3.92699081698724
x37 = -76.5885136358376
x38 = 11.3760806646766
x39 = 38.484510006475
x40 = 80.4911190436521
x41 = 52.216785161344
x42 = -90.3207887907066
x43 = -7.47347525686212
x44 = -42.0309944463498
x45 = -20.0398458712213
x46 = 98.174770424681
x47 = -92.2964769037865
x48 = -230.526553661737
x49 = -26.3230311784009
x50 = -18.0641577581413
x51 = 76.1836218495525
x52 = -40.0553063332699
x53 = -70.305328328658
x54 = 22.776546738526
x55 = 58.4999704685235
x56 = 30.2256365862154
x57 = 14.5176733182664
x58 = 86.7743043508317
x59 = -68.329640215578
x60 = -86.0132915966069
x61 = -33.7721210260903
x62 = 17.6592659718562
x63 = -64.0221430214784
x64 = -13.7566605640417
x65 = 83.6327116972419
x66 = -49.4800842940392
x67 = -87.1791961371168
x68 = -10.6150679104519
x69 = 96.1990823116011
x70 = -35.7478091391703
x71 = 25.9181393921158
x72 = -99.7455667514759
x73 = 54.1924732744239
x74 = -98.5796622109661
x75 = -24.3473430653209
x76 = 63.6172512351933
x77 = -48.3141797535294
x78 = 19.6349540849362
x79 = -79.7301062894274
x80 = -93.4623814442964
x81 = -95.4380695573763
x82 = -32.6062164855805
x83 = -43.1968989868597
x84 = 33.3672292398052
x85 = -11.7809724509617
x86 = 39.6504145469848
x87 = -62.0464549083984
x88 = 1.95130270390726
x89 = 69.9004365423729
x90 = 1235.43131102419
x91 = -2.35619449019234
x92 = 47.9092879672443
x93 = -4.33188260327232
x93 = -4.33188260327232