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4*sin(x)*cos(x)-sin(x)-sqrt3*cos(x)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
___ 4*sin(x)*cos(x) - sin(x) - \/ 3 *cos(x) = 0
$$\left(- \sin{\left(x \right)} + 4 \sin{\left(x \right)} \cos{\left(x \right)}\right) - \sqrt{3} \cos{\left(x \right)} = 0$$
Respuesta rápida
[src]
/ / __________________________________________________________________________________________________________________________ \\ / / __________________________________________________________________________________________________________________________ \\
| | / 3 ___ 3 ____ ______________ || | | / 3 ___ 3 ____ ______________ ||
| | ___ / 107*\/ 2 2*\/ 18 2/3 3 ___ 3 / ___ || | | ___ / 107*\/ 2 2*\/ 18 2/3 3 ___ 3 / ___ ||
| | \/ 6 * / 25 - ---------------------------------------------------------------- - ----------------- - 2 *\/ 3 *\/ -3 + I*\/ 3 || | | \/ 6 * / 25 - ---------------------------------------------------------------- - ----------------- - 2 *\/ 3 *\/ -3 + I*\/ 3 ||
| | / _________________________________________________________ ______________ _________________________________________________________|| | | / _________________________________________________________ ______________ _________________________________________________________||
| | / / ______________ 2/3 3 / ___ / ______________ 2/3 || | | / / ______________ 2/3 3 / ___ / ______________ 2/3 ||
| | / / 2/3 3 ___ 3 / ___ 8*3 \/ -3 + I*\/ 3 2/3 ___ / 2/3 3 ___ 3 / ___ 8*3 || | | / / 2/3 3 ___ 3 / ___ 8*3 \/ -3 + I*\/ 3 2/3 ___ / 2/3 3 ___ 3 / ___ 8*3 ||
| | / / 25*2 + 4*\/ 6 *\/ -3 + I*\/ 3 + ----------------- 2 *\/ 3 * / 25*2 + 4*\/ 6 *\/ -3 + I*\/ 3 + ----------------- || | | / / 25*2 + 4*\/ 6 *\/ -3 + I*\/ 3 + ----------------- 2 *\/ 3 * / 25*2 + 4*\/ 6 *\/ -3 + I*\/ 3 + ----------------- ||
| | / / ______________ / ______________ || | | / / ______________ / ______________ ||
| | ___ / / 3 / ___ / 3 / ___ || | | ___ / / 3 / ___ / 3 / ___ ||
| | 5*\/ 3 \/ \/ \/ -3 + I*\/ 3 \/ \/ -3 + I*\/ 3 || | | 5*\/ 3 \/ \/ \/ -3 + I*\/ 3 \/ \/ -3 + I*\/ 3 ||
x1 = - 2*re|atan|- ------- + ------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------|| - 2*I*im|atan|- ------- + ------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------||
\ \ 6 6 12 // \ \ 6 6 12 //
$$x_{1} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{5 \sqrt{3}}{6} + \frac{\sqrt{6} \sqrt{25 - 2^{\frac{2}{3}} \sqrt[3]{3} \sqrt[3]{-3 + \sqrt{3} i} - \frac{107 \sqrt[3]{2}}{\sqrt{25 \cdot 2^{\frac{2}{3}} + \frac{8 \cdot 3^{\frac{2}{3}}}{\sqrt[3]{-3 + \sqrt{3} i}} + 4 \sqrt[3]{6} \sqrt[3]{-3 + \sqrt{3} i}}} - \frac{2 \sqrt[3]{18}}{\sqrt[3]{-3 + \sqrt{3} i}}}}{6} + \frac{2^{\frac{2}{3}} \sqrt{3} \sqrt{25 \cdot 2^{\frac{2}{3}} + \frac{8 \cdot 3^{\frac{2}{3}}}{\sqrt[3]{-3 + \sqrt{3} i}} + 4 \sqrt[3]{6} \sqrt[3]{-3 + \sqrt{3} i}}}{12} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{5 \sqrt{3}}{6} + \frac{\sqrt{6} \sqrt{25 - 2^{\frac{2}{3}} \sqrt[3]{3} \sqrt[3]{-3 + \sqrt{3} i} - \frac{107 \sqrt[3]{2}}{\sqrt{25 \cdot 2^{\frac{2}{3}} + \frac{8 \cdot 3^{\frac{2}{3}}}{\sqrt[3]{-3 + \sqrt{3} i}} + 4 \sqrt[3]{6} \sqrt[3]{-3 + \sqrt{3} i}}} - \frac{2 \sqrt[3]{18}}{\sqrt[3]{-3 + \sqrt{3} i}}}}{6} + \frac{2^{\frac{2}{3}} \sqrt{3} \sqrt{25 \cdot 2^{\frac{2}{3}} + \frac{8 \cdot 3^{\frac{2}{3}}}{\sqrt[3]{-3 + \sqrt{3} i}} + 4 \sqrt[3]{6} \sqrt[3]{-3 + \sqrt{3} i}}}{12} \right)}\right)}$$
/ / __________________________________________________________________________________________________________________________ \\ / / __________________________________________________________________________________________________________________________ \\
| | / 3 ____ 3 ___ ______________ || | | / 3 ____ 3 ___ ______________ ||
| | ___ / 2*\/ 18 107*\/ 2 2/3 3 ___ 3 / ___ || | | ___ / 2*\/ 18 107*\/ 2 2/3 3 ___ 3 / ___ ||
| | \/ 6 * / 25 - ----------------- + ---------------------------------------------------------------- - 2 *\/ 3 *\/ -3 + I*\/ 3 || | | \/ 6 * / 25 - ----------------- + ---------------------------------------------------------------- - 2 *\/ 3 *\/ -3 + I*\/ 3 ||
| | / ______________ _________________________________________________________ _________________________________________________________|| | | / ______________ _________________________________________________________ _________________________________________________________||
| | / 3 / ___ / ______________ 2/3 / ______________ 2/3 || | | / 3 / ___ / ______________ 2/3 / ______________ 2/3 ||
| | / \/ -3 + I*\/ 3 / 2/3 3 ___ 3 / ___ 8*3 2/3 ___ / 2/3 3 ___ 3 / ___ 8*3 || | | / \/ -3 + I*\/ 3 / 2/3 3 ___ 3 / ___ 8*3 2/3 ___ / 2/3 3 ___ 3 / ___ 8*3 ||
| | / / 25*2 + 4*\/ 6 *\/ -3 + I*\/ 3 + ----------------- 2 *\/ 3 * / 25*2 + 4*\/ 6 *\/ -3 + I*\/ 3 + ----------------- || | | / / 25*2 + 4*\/ 6 *\/ -3 + I*\/ 3 + ----------------- 2 *\/ 3 * / 25*2 + 4*\/ 6 *\/ -3 + I*\/ 3 + ----------------- ||
| | / / ______________ / ______________ || | | / / ______________ / ______________ ||
| | ___ / / 3 / ___ / 3 / ___ || | | ___ / / 3 / ___ / 3 / ___ ||
| |5*\/ 3 \/ \/ \/ -3 + I*\/ 3 \/ \/ -3 + I*\/ 3 || | |5*\/ 3 \/ \/ \/ -3 + I*\/ 3 \/ \/ -3 + I*\/ 3 ||
x2 = 2*re|atan|------- - ------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------|| + 2*I*im|atan|------- - ------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------||
\ \ 6 6 12 // \ \ 6 6 12 //
$$x_{2} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{5 \sqrt{3}}{6} - \frac{\sqrt{6} \sqrt{25 - 2^{\frac{2}{3}} \sqrt[3]{3} \sqrt[3]{-3 + \sqrt{3} i} + \frac{107 \sqrt[3]{2}}{\sqrt{25 \cdot 2^{\frac{2}{3}} + \frac{8 \cdot 3^{\frac{2}{3}}}{\sqrt[3]{-3 + \sqrt{3} i}} + 4 \sqrt[3]{6} \sqrt[3]{-3 + \sqrt{3} i}}} - \frac{2 \sqrt[3]{18}}{\sqrt[3]{-3 + \sqrt{3} i}}}}{6} + \frac{2^{\frac{2}{3}} \sqrt{3} \sqrt{25 \cdot 2^{\frac{2}{3}} + \frac{8 \cdot 3^{\frac{2}{3}}}{\sqrt[3]{-3 + \sqrt{3} i}} + 4 \sqrt[3]{6} \sqrt[3]{-3 + \sqrt{3} i}}}{12} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{5 \sqrt{3}}{6} - \frac{\sqrt{6} \sqrt{25 - 2^{\frac{2}{3}} \sqrt[3]{3} \sqrt[3]{-3 + \sqrt{3} i} + \frac{107 \sqrt[3]{2}}{\sqrt{25 \cdot 2^{\frac{2}{3}} + \frac{8 \cdot 3^{\frac{2}{3}}}{\sqrt[3]{-3 + \sqrt{3} i}} + 4 \sqrt[3]{6} \sqrt[3]{-3 + \sqrt{3} i}}} - \frac{2 \sqrt[3]{18}}{\sqrt[3]{-3 + \sqrt{3} i}}}}{6} + \frac{2^{\frac{2}{3}} \sqrt{3} \sqrt{25 \cdot 2^{\frac{2}{3}} + \frac{8 \cdot 3^{\frac{2}{3}}}{\sqrt[3]{-3 + \sqrt{3} i}} + 4 \sqrt[3]{6} \sqrt[3]{-3 + \sqrt{3} i}}}{12} \right)}\right)}$$
/ __________________________________________________________________________________________________________________________ \
| / 3 ____ 3 ___ ______________ |
| ___ / 2*\/ 18 107*\/ 2 2/3 3 ___ 3 / ___ |
| \/ 6 * / 25 - ----------------- + ---------------------------------------------------------------- - 2 *\/ 3 *\/ -3 + I*\/ 3 |
| / ______________ _________________________________________________________ _________________________________________________________|
| / 3 / ___ / ______________ 2/3 / ______________ 2/3 |
| / \/ -3 + I*\/ 3 / 2/3 3 ___ 3 / ___ 8*3 2/3 ___ / 2/3 3 ___ 3 / ___ 8*3 |
| / / 25*2 + 4*\/ 6 *\/ -3 + I*\/ 3 + ----------------- 2 *\/ 3 * / 25*2 + 4*\/ 6 *\/ -3 + I*\/ 3 + ----------------- |
| / / ______________ / ______________ |
| ___ / / 3 / ___ / 3 / ___ |
|5*\/ 3 \/ \/ \/ -3 + I*\/ 3 \/ \/ -3 + I*\/ 3 |
x3 = 2*atan|------- + ------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------|
\ 6 6 12 /
$$x_{3} = 2 \operatorname{atan}{\left(\frac{5 \sqrt{3}}{6} + \frac{\sqrt{6} \sqrt{25 - 2^{\frac{2}{3}} \sqrt[3]{3} \sqrt[3]{-3 + \sqrt{3} i} + \frac{107 \sqrt[3]{2}}{\sqrt{25 \cdot 2^{\frac{2}{3}} + \frac{8 \cdot 3^{\frac{2}{3}}}{\sqrt[3]{-3 + \sqrt{3} i}} + 4 \sqrt[3]{6} \sqrt[3]{-3 + \sqrt{3} i}}} - \frac{2 \sqrt[3]{18}}{\sqrt[3]{-3 + \sqrt{3} i}}}}{6} + \frac{2^{\frac{2}{3}} \sqrt{3} \sqrt{25 \cdot 2^{\frac{2}{3}} + \frac{8 \cdot 3^{\frac{2}{3}}}{\sqrt[3]{-3 + \sqrt{3} i}} + 4 \sqrt[3]{6} \sqrt[3]{-3 + \sqrt{3} i}}}{12} \right)}$$
/ / __________________________________________________________________________________________________________________________ \\ / / __________________________________________________________________________________________________________________________ \\
| | / 3 ___ 3 ____ ______________ || | | / 3 ___ 3 ____ ______________ ||
| | ___ / 107*\/ 2 2*\/ 18 2/3 3 ___ 3 / ___ || | | ___ / 107*\/ 2 2*\/ 18 2/3 3 ___ 3 / ___ ||
| | \/ 6 * / 25 - ---------------------------------------------------------------- - ----------------- - 2 *\/ 3 *\/ -3 + I*\/ 3 || | | \/ 6 * / 25 - ---------------------------------------------------------------- - ----------------- - 2 *\/ 3 *\/ -3 + I*\/ 3 ||
| | / _________________________________________________________ ______________ _________________________________________________________|| | | / _________________________________________________________ ______________ _________________________________________________________||
| | / / ______________ 2/3 3 / ___ / ______________ 2/3 || | | / / ______________ 2/3 3 / ___ / ______________ 2/3 ||
| | / / 2/3 3 ___ 3 / ___ 8*3 \/ -3 + I*\/ 3 2/3 ___ / 2/3 3 ___ 3 / ___ 8*3 || | | / / 2/3 3 ___ 3 / ___ 8*3 \/ -3 + I*\/ 3 2/3 ___ / 2/3 3 ___ 3 / ___ 8*3 ||
| | / / 25*2 + 4*\/ 6 *\/ -3 + I*\/ 3 + ----------------- 2 *\/ 3 * / 25*2 + 4*\/ 6 *\/ -3 + I*\/ 3 + ----------------- || | | / / 25*2 + 4*\/ 6 *\/ -3 + I*\/ 3 + ----------------- 2 *\/ 3 * / 25*2 + 4*\/ 6 *\/ -3 + I*\/ 3 + ----------------- ||
| | / / ______________ / ______________ || | | / / ______________ / ______________ ||
| | ___ / / 3 / ___ / 3 / ___ || | | ___ / / 3 / ___ / 3 / ___ ||
| |5*\/ 3 \/ \/ \/ -3 + I*\/ 3 \/ \/ -3 + I*\/ 3 || | |5*\/ 3 \/ \/ \/ -3 + I*\/ 3 \/ \/ -3 + I*\/ 3 ||
x4 = 2*re|atan|------- + ------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------|| + 2*I*im|atan|------- + ------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------||
\ \ 6 6 12 // \ \ 6 6 12 //
$$x_{4} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{5 \sqrt{3}}{6} - \frac{2^{\frac{2}{3}} \sqrt{3} \sqrt{25 \cdot 2^{\frac{2}{3}} + \frac{8 \cdot 3^{\frac{2}{3}}}{\sqrt[3]{-3 + \sqrt{3} i}} + 4 \sqrt[3]{6} \sqrt[3]{-3 + \sqrt{3} i}}}{12} + \frac{\sqrt{6} \sqrt{25 - 2^{\frac{2}{3}} \sqrt[3]{3} \sqrt[3]{-3 + \sqrt{3} i} - \frac{107 \sqrt[3]{2}}{\sqrt{25 \cdot 2^{\frac{2}{3}} + \frac{8 \cdot 3^{\frac{2}{3}}}{\sqrt[3]{-3 + \sqrt{3} i}} + 4 \sqrt[3]{6} \sqrt[3]{-3 + \sqrt{3} i}}} - \frac{2 \sqrt[3]{18}}{\sqrt[3]{-3 + \sqrt{3} i}}}}{6} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{5 \sqrt{3}}{6} - \frac{2^{\frac{2}{3}} \sqrt{3} \sqrt{25 \cdot 2^{\frac{2}{3}} + \frac{8 \cdot 3^{\frac{2}{3}}}{\sqrt[3]{-3 + \sqrt{3} i}} + 4 \sqrt[3]{6} \sqrt[3]{-3 + \sqrt{3} i}}}{12} + \frac{\sqrt{6} \sqrt{25 - 2^{\frac{2}{3}} \sqrt[3]{3} \sqrt[3]{-3 + \sqrt{3} i} - \frac{107 \sqrt[3]{2}}{\sqrt{25 \cdot 2^{\frac{2}{3}} + \frac{8 \cdot 3^{\frac{2}{3}}}{\sqrt[3]{-3 + \sqrt{3} i}} + 4 \sqrt[3]{6} \sqrt[3]{-3 + \sqrt{3} i}}} - \frac{2 \sqrt[3]{18}}{\sqrt[3]{-3 + \sqrt{3} i}}}}{6} \right)}\right)}$$
x4 = 2*re(atan(5*sqrt(3)/6 - 2^(2/3)*sqrt(3)*sqrt(25*2^(2/3) + 8*3^(2/3)/(-3 + sqrt(3)*i)^(1/3) + 4*6^(1/3)*(-3 + sqrt(3)*i)^(1/3))/12 + sqrt(6)*sqrt(25 - 2^(2/3)*3^(1/3)*(-3 + sqrt(3)*i)^(1/3) - 107*2^(1/3)/sqrt(25*2^(2/3) + 8*3^(2/3)/(-3 + sqrt(3)*i)^(1/3) + 4*6^(1/3)*(-3 + sqrt(3)*i)^(1/3)) - 2*18^(1/3)/(-3 + sqrt(3)*i)^(1/3))/6)) + 2*i*im(atan(5*sqrt(3)/6 - 2^(2/3)*sqrt(3)*sqrt(25*2^(2/3) + 8*3^(2/3)/(-3 + sqrt(3)*i)^(1/3) + 4*6^(1/3)*(-3 + sqrt(3)*i)^(1/3))/12 + sqrt(6)*sqrt(25 - 2^(2/3)*3^(1/3)*(-3 + sqrt(3)*i)^(1/3) - 107*2^(1/3)/sqrt(25*2^(2/3) + 8*3^(2/3)/(-3 + sqrt(3)*i)^(1/3) + 4*6^(1/3)*(-3 + sqrt(3)*i)^(1/3)) - 2*18^(1/3)/(-3 + sqrt(3)*i)^(1/3))/6))
Respuesta numérica
[src]
x1 = 42.5860337486616
x2 = 23.7364778271229
x3 = -1.39626340159546
x4 = -91.4552528045029
x5 = 86.5683308989187
x6 = 21.6420827247297
x7 = -17.8023583703422
x8 = 94.9459113084915
x9 = 50.9636141582344
x10 = 76.0963553869528
x11 = -57.9449311662117
x12 = -39.095375244673
x13 = -11.8682389135614
x14 = -70.5113017805709
x15 = 17.4532925199433
x16 = 84.4739357965256
x17 = -13.9626340159546
x18 = 78.190750489346
x19 = 88.6627260013119
x20 = -5.58505360638185
x21 = -45.3785605518526
x22 = 13.6135681655558
x23 = -3.49065850398866
x24 = -43.2841654494594
x25 = 65.6243798749868
x26 = 6.98131700797732
x27 = -87.2664625997165
x28 = -55.8505360638185
x29 = 4.88692190558412
x30 = 63.8790506229925
x31 = -89.3608577021097
x32 = 48.8692190558412
x33 = -101.927228316469
x34 = 57.5958653158129
x35 = -37.0009801422798
x36 = 70.162235930172
x37 = 19.8967534727354
x38 = 74.0019602845596
x39 = 51.3126800086333
x40 = -80.9832772925369
x41 = 36.3028484414821
x42 = -20.2458193231342
x43 = 15.3588974175501
x44 = 32.1140582366957
x45 = 30.0196631343025
x46 = 34.2084533390889
x47 = 0.698131700797732
x48 = -30.3687289847013
x49 = -64.2281164733913
x50 = -68.0678408277789
x51 = 82.3795406941324
x52 = -97.7384381116825
x53 = -5503.02313153812
x54 = 59.3411945678072
x55 = -53.7561409614254
x56 = -16.0570291183478
x57 = -66.3225115757845
x58 = -36.6519142918809
x59 = 71.9075651821664
x60 = -9.77384381116824
x61 = -28.623399732707
x62 = -93.5496479068961
x63 = -26.5290046303138
x64 = 38.3972435438752
x65 = -99.8328332140756
x66 = 67.71877497738
x67 = -68.4169066781777
x68 = 92.8515162060983
x69 = -22.3402144255274
x70 = -24.4346095279206
x71 = -49.567350756639
x72 = -61.7846555205993
x73 = 126.710903694788
x74 = -95.6440430092893
x75 = 44.6804288510548
x76 = -7.67944870877505
x77 = 80.2851455917392
x78 = -24.0855436775217
x79 = 61.4355896702004
x80 = -47.4729556542458
x81 = -83.0776723949301
x82 = -60.0393262686049
x83 = -51.6617458590322
x84 = 27.9252680319093
x85 = -72.6056968829641
x86 = 26.1799387799149
x87 = 40.4916386462684
x88 = 9.07571211037051
x89 = -74.3510261349584
x90 = -80.634211442138
x90 = -80.634211442138