cos(x)=-(4/5) (уравнение)

Найду корень уравнения: cos(x)=-(4/5)

Вы ввели

cos(x) = -4/5

$$\cos{\left(x \right)} = - \frac{4}{5}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = - \frac{4}{5}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(- \frac{4}{5} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{4}{5} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(- \frac{4}{5} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{4}{5} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -acos(-4/5) + 2*pi

$$x_{1} = - \operatorname{acos}{\left(- \frac{4}{5} \right)} + 2 \pi$$

x2 = acos(-4/5)

$$x_{2} = \operatorname{acos}{\left(- \frac{4}{5} \right)}$$

Сумма и произведение корней

сумма

0 + -acos(-4/5) + 2*pi + acos(-4/5)

$$\operatorname{acos}{\left(- \frac{4}{5} \right)} + \left(0 + \left(- \operatorname{acos}{\left(- \frac{4}{5} \right)} + 2 \pi\right)\right)$$

=

2*pi

$$2 \pi$$

произведение

1*(-acos(-4/5) + 2*pi)*acos(-4/5)

$$1 \left(- \operatorname{acos}{\left(- \frac{4}{5} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{4}{5} \right)}$$

=

(-acos(-4/5) + 2*pi)*acos(-4/5)

$$\left(- \operatorname{acos}{\left(- \frac{4}{5} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{4}{5} \right)}$$

Численный ответ

x1 = 91.7496880628973

x2 = 85.4665027557177

x3 = 52.7635740022332

x4 = 8.7812768519761

x5 = 59.0467593094128

x6 = 90.4626858453107

x7 = -41.4842056054606

x8 = 3.78509376238308

x9 = -8.7812768519761

x10 = 79.1833174485381

x11 = 71.613129923772

x12 = 72.9001321413585

x13 = -16.3514643767422

x14 = -27.6308327735149

x15 = -65.3299446165924

x16 = -52.7635740022332

x17 = 84.1795005381311

x18 = -256822.701339421

x19 = -77.8963152309515

x20 = -33.9140180806944

x21 = -59.0467593094128

x22 = -60.3337615269994

x23 = 35.201020298281

x24 = 544.139030179828

x25 = 41.4842056054606

x26 = 16.3514643767422

x27 = 22.6346496839218

x28 = 28.9178349911014

x29 = -46.4803886950536

x30 = -35.201020298281

x31 = 33.9140180806944

x32 = -28.9178349911014

x33 = -40.197203387874

x34 = -22.6346496839218

x35 = 66.6169468341789

x36 = 3653.02875501614

x37 = 46.4803886950536

x38 = -47.7673909126402

x39 = -147.011353609927

x40 = 40.197203387874

x41 = 98.0328733700769

x42 = 77.8963152309515

x43 = -98.0328733700769

x44 = -21.3476474663353

x45 = -2.49809154479651

x46 = -217.413394206489

x47 = -72.9001321413585

x48 = 47.7673909126402

x49 = -90.4626858453107

x50 = 65.3299446165924

x51 = 27.6308327735149

x52 = -79.1833174485381

x53 = 96.7458711524903

x54 = -15.0644621591557

x55 = -54.0505762198198

x56 = -3.78509376238308

x57 = 60.3337615269994

x58 = 5287.94393710042

x59 = -85.4665027557177

x60 = 54.0505762198198

x61 = -91.7496880628973

x62 = -66.6169468341789

x63 = -71.613129923772

x64 = 21.3476474663353

x65 = -96.7458711524903

x66 = 15.0644621591557

x67 = -84.1795005381311

x68 = 2.49809154479651

x69 = -10.0682790695627

x70 = 10.0682790695627

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