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(4cosx)-(sin^2x)-4=0

(4cosx)-(sin^2x)-4=0 уравнение

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Численное решение:

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Решение

Вы ввели [src]
              2           
4*cos(x) - sin (x) - 4 = 0
$$- \sin^{2}{\left(x \right)} + 4 \cos{\left(x \right)} - 4 = 0$$
График
Быстрый ответ [src]
x_1 = 0
$$x_{1} = 0$$
          /     /  ___\\         /     /  ___\\
          |     |\/ 6 ||         |     |\/ 6 ||
x_2 = 2*im|atanh|-----|| - 2*I*re|atanh|-----||
          \     \  2  //         \     \  2  //
$$x_{2} = 2 \operatorname{im}{\left(\operatorname{atanh}{\left(\frac{\sqrt{6}}{2} \right)}\right)} - 2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\frac{\sqrt{6}}{2} \right)}\right)}$$
            /     /  ___\\         /     /  ___\\
            |     |\/ 6 ||         |     |\/ 6 ||
x_3 = - 2*im|atanh|-----|| + 2*I*re|atanh|-----||
            \     \  2  //         \     \  2  //
$$x_{3} = - 2 \operatorname{im}{\left(\operatorname{atanh}{\left(\frac{\sqrt{6}}{2} \right)}\right)} + 2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\frac{\sqrt{6}}{2} \right)}\right)}$$
Сумма и произведение корней [src]
сумма
        /     /  ___\\         /     /  ___\\         /     /  ___\\         /     /  ___\\
        |     |\/ 6 ||         |     |\/ 6 ||         |     |\/ 6 ||         |     |\/ 6 ||
0 + 2*im|atanh|-----|| - 2*I*re|atanh|-----|| + - 2*im|atanh|-----|| + 2*I*re|atanh|-----||
        \     \  2  //         \     \  2  //         \     \  2  //         \     \  2  //
$$\left(0\right) + \left(2 \operatorname{im}{\left(\operatorname{atanh}{\left(\frac{\sqrt{6}}{2} \right)}\right)} - 2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\frac{\sqrt{6}}{2} \right)}\right)}\right) + \left(- 2 \operatorname{im}{\left(\operatorname{atanh}{\left(\frac{\sqrt{6}}{2} \right)}\right)} + 2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\frac{\sqrt{6}}{2} \right)}\right)}\right)$$
=
0
$$0$$
произведение
        /     /  ___\\         /     /  ___\\         /     /  ___\\         /     /  ___\\
        |     |\/ 6 ||         |     |\/ 6 ||         |     |\/ 6 ||         |     |\/ 6 ||
0 * 2*im|atanh|-----|| - 2*I*re|atanh|-----|| * - 2*im|atanh|-----|| + 2*I*re|atanh|-----||
        \     \  2  //         \     \  2  //         \     \  2  //         \     \  2  //
$$\left(0\right) * \left(2 \operatorname{im}{\left(\operatorname{atanh}{\left(\frac{\sqrt{6}}{2} \right)}\right)} - 2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\frac{\sqrt{6}}{2} \right)}\right)}\right) * \left(- 2 \operatorname{im}{\left(\operatorname{atanh}{\left(\frac{\sqrt{6}}{2} \right)}\right)} + 2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\frac{\sqrt{6}}{2} \right)}\right)}\right)$$
=
0
$$0$$
Численный ответ [src]
x1 = 3.6542214453576e-9
x2 = -25.1327415128681
x3 = 43.9822971694522
x4 = -6.28318561085183
x5 = -62.8318527166215
x6 = -18.8495555631251
x7 = -18.8495554932831
x8 = 94.2477796093524
x9 = 62.8318527993111
x10 = 37.6991120272784
x11 = 100.530964762008
x12 = -94.2477794477884
x13 = 56.5486676037551
x14 = 25.1327415901841
x15 = -50.2654822892671
x16 = -31.4159267123914
x17 = -75.3982233514527
x18 = -25.1327408470065
x19 = 69.1150384791184
x20 = 94.2477795996487
x21 = 6.28318536397799
x22 = -37.6991118772263
x23 = 31.4159268278413
x24 = 18.849555643152
x25 = 69.1150380303718
x26 = -31.4159262080502
x27 = 25.1327411190543
x28 = -37.699111757691
x29 = -43.9822971102957
x30 = -43.9822971745523
x31 = -81.6814090381547
x32 = 81.6814086730756
x33 = -87.9645943586678
x34 = -81.6814088816483
x35 = 12.5663704456227
x36 = 50.2654824831612
x37 = -69.1150386687467
x38 = -12.566370328105
x39 = 81.6814091853186
x40 = -50.2654827516428
x41 = -56.5486674841957
x42 = -12.5663709884597
x43 = 0.0
x44 = -18.8495562765773
x45 = 18.849556302627
x46 = -62.8318534297581
x47 = 87.9645943358564
x48 = 31.4159261609886
x49 = 69.1150387433025
x50 = -94.2477798915732
x51 = 62.8318534519676
x52 = 37.6991115307392
x53 = 75.3982239836414
x54 = -87.9645942211314
x55 = 75.3982233107482
x56 = -62.8318524720618
x57 = 6.2831852842226
x58 = 697.433569577321
x59 = 56.5486680767914
x60 = -75.3982238702881
x61 = 50.2654824463419
x62 = 25.1327408768009
x63 = -69.1150379969225
x64 = -100.530964640429
x65 = 12.5663709347131
x66 = 87.9645942399983
x67 = -69.1150387794245
x68 = 43.9822971204917
x69 = -6.28318513091445
x70 = -56.5486681375837
x70 = -56.5486681375837
График
(4cosx)-(sin^2x)-4=0 уравнение