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sqrt(3)/2-cos(x)-1/2*sin(x)=1 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
  ___                      
\/ 3             sin(x)    
----- - cos(x) - ------ = 1
  2                2       
$$\left(- \cos{\left(x \right)} + \frac{\sqrt{3}}{2}\right) - \frac{\sin{\left(x \right)}}{2} = 1$$
Gráfica
Respuesta rápida [src]
           /                 ______________\
           |  ___     ___   /          ___ |
           |\/ 3    \/ 6 *\/  -1 + 2*\/ 3  |
x1 = 2*atan|----- + -----------------------|
           \  3                3           /
$$x_{1} = 2 \operatorname{atan}{\left(\frac{\sqrt{3}}{3} + \frac{\sqrt{6} \sqrt{-1 + 2 \sqrt{3}}}{3} \right)}$$
           /                 ______________\
           |  ___     ___   /          ___ |
           |\/ 3    \/ 6 *\/  -1 + 2*\/ 3  |
x2 = 2*atan|----- - -----------------------|
           \  3                3           /
$$x_{2} = 2 \operatorname{atan}{\left(- \frac{\sqrt{6} \sqrt{-1 + 2 \sqrt{3}}}{3} + \frac{\sqrt{3}}{3} \right)}$$
x2 = 2*atan(-sqrt(6)*sqrt(-1 + 2*sqrt(3))/3 + sqrt(3)/3)
Suma y producto de raíces [src]
suma
      /                 ______________\         /                 ______________\
      |  ___     ___   /          ___ |         |  ___     ___   /          ___ |
      |\/ 3    \/ 6 *\/  -1 + 2*\/ 3  |         |\/ 3    \/ 6 *\/  -1 + 2*\/ 3  |
2*atan|----- + -----------------------| + 2*atan|----- - -----------------------|
      \  3                3           /         \  3                3           /
$$2 \operatorname{atan}{\left(- \frac{\sqrt{6} \sqrt{-1 + 2 \sqrt{3}}}{3} + \frac{\sqrt{3}}{3} \right)} + 2 \operatorname{atan}{\left(\frac{\sqrt{3}}{3} + \frac{\sqrt{6} \sqrt{-1 + 2 \sqrt{3}}}{3} \right)}$$
=
      /                 ______________\         /                 ______________\
      |  ___     ___   /          ___ |         |  ___     ___   /          ___ |
      |\/ 3    \/ 6 *\/  -1 + 2*\/ 3  |         |\/ 3    \/ 6 *\/  -1 + 2*\/ 3  |
2*atan|----- - -----------------------| + 2*atan|----- + -----------------------|
      \  3                3           /         \  3                3           /
$$2 \operatorname{atan}{\left(- \frac{\sqrt{6} \sqrt{-1 + 2 \sqrt{3}}}{3} + \frac{\sqrt{3}}{3} \right)} + 2 \operatorname{atan}{\left(\frac{\sqrt{3}}{3} + \frac{\sqrt{6} \sqrt{-1 + 2 \sqrt{3}}}{3} \right)}$$
producto
      /                 ______________\       /                 ______________\
      |  ___     ___   /          ___ |       |  ___     ___   /          ___ |
      |\/ 3    \/ 6 *\/  -1 + 2*\/ 3  |       |\/ 3    \/ 6 *\/  -1 + 2*\/ 3  |
2*atan|----- + -----------------------|*2*atan|----- - -----------------------|
      \  3                3           /       \  3                3           /
$$2 \operatorname{atan}{\left(\frac{\sqrt{3}}{3} + \frac{\sqrt{6} \sqrt{-1 + 2 \sqrt{3}}}{3} \right)} 2 \operatorname{atan}{\left(- \frac{\sqrt{6} \sqrt{-1 + 2 \sqrt{3}}}{3} + \frac{\sqrt{3}}{3} \right)}$$
=
      /                 ______________\     /                 ______________\
      |  ___     ___   /          ___ |     |  ___     ___   /          ___ |
      |\/ 3    \/ 6 *\/  -1 + 2*\/ 3  |     |\/ 3    \/ 6 *\/  -1 + 2*\/ 3  |
4*atan|----- - -----------------------|*atan|----- + -----------------------|
      \  3                3           /     \  3                3           /
$$4 \operatorname{atan}{\left(\frac{\sqrt{3}}{3} + \frac{\sqrt{6} \sqrt{-1 + 2 \sqrt{3}}}{3} \right)} \operatorname{atan}{\left(- \frac{\sqrt{6} \sqrt{-1 + 2 \sqrt{3}}}{3} + \frac{\sqrt{3}}{3} \right)}$$
4*atan(sqrt(3)/3 - sqrt(6)*sqrt(-1 + 2*sqrt(3))/3)*atan(sqrt(3)/3 + sqrt(6)*sqrt(-1 + 2*sqrt(3))/3)
Respuesta numérica [src]
x1 = 21.004119029666
x2 = 99.3036970247478
x3 = 42.7550292601315
x4 = -22.9781781205911
x5 = -4.12862219905238
x6 = 2.15456310812721
x7 = 9335.58609857874
x8 = -48.1109193493095
x9 = 86.7373264103886
x10 = -13.7936385044848
x11 = -29.2613634277707
x12 = 5.05591741705399
x13 = 30.1886586457723
x14 = -64.0591209619215
x15 = -112083.588131669
x16 = 83.8359721014618
x17 = 58.7032308727435
x18 = -95.4750474978194
x19 = -60.6772899636687
x20 = -35.5445487349503
x21 = -76.6254915762806
x22 = -89.1918621906398
x23 = 61.6045851816703
x24 = 36.4718439529519
x25 = -98.3764018067462
x26 = 39.8536749512047
x27 = -16.6949928134116
x28 = 90.1191574086414
x29 = -85.810031192387
x30 = -51.4927503475623
x31 = -32.6431944260235
x32 = -101.758232804999
x33 = 14.7209337224864
x34 = 52.4200455655639
x35 = -41.8277340421299
x36 = 17.6222880314132
x37 = -265.121050791668
x38 = -82.9086768834602
x39 = -10.411807506232
x40 = -38.9263797332031
x41 = -20.0768238116644
x42 = -57.7759356547419
x43 = 67.8877704888499
x44 = -1.22726789012559
x45 = -26.3600091188439
x46 = 96.402342715821
x47 = -54.3941046564891
x48 = 64.9864161799231
x49 = 33.5704896440251
x50 = -45.2095650403827
x51 = 46.1368602583843
x52 = -70.342306269101
x53 = -7.51045319730518
x54 = -79.5268458852074
x55 = 55.3213998744907
x56 = 23.9054733385928
x57 = -92.0932164995666
x58 = 8.43774841530679
x59 = 27.2873043368456
x60 = -66.9604752708482
x61 = -73.2436605780278
x62 = 93.0205117175682
x63 = 49.0382145673111
x64 = 77.5527867942822
x65 = 80.454141103209
x66 = 74.1709557960294
x67 = 71.2696014871027
x68 = 11.3391027242336
x68 = 11.3391027242336