cos(x)=-0.7 (уравнение)

Найду корень уравнения: cos(x)=-0.7

Вы ввели

cos(x) = -7/10

$$\cos{\left(x \right)} = - \frac{7}{10}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = - \frac{7}{10}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(- \frac{7}{10} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{7}{10} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(- \frac{7}{10} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{7}{10} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -acos(-7/10) + 2*pi

$$x_{1} = - \operatorname{acos}{\left(- \frac{7}{10} \right)} + 2 \pi$$

x2 = acos(-7/10)

$$x_{2} = \operatorname{acos}{\left(- \frac{7}{10} \right)}$$

Сумма и произведение корней

сумма

0 + -acos(-7/10) + 2*pi + acos(-7/10)

$$\operatorname{acos}{\left(- \frac{7}{10} \right)} + \left(0 + \left(- \operatorname{acos}{\left(- \frac{7}{10} \right)} + 2 \pi\right)\right)$$

=

2*pi

$$2 \pi$$

произведение

1*(-acos(-7/10) + 2*pi)*acos(-7/10)

$$1 \left(- \operatorname{acos}{\left(- \frac{7}{10} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{7}{10} \right)}$$

=

(-acos(-7/10) + 2*pi)*acos(-7/10)

$$\left(- \operatorname{acos}{\left(- \frac{7}{10} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{7}{10} \right)}$$

Численный ответ

x1 = 77.7444175095607

x2 = -46.3284909736628

x3 = -84.0276028167403

x4 = 16.5033620981331

x5 = 54.2024739412106

x6 = -98.1847710914677

x7 = -14.9125644377648

x8 = 35.3529180196719

x9 = 58.8948615880219

x10 = 21.1957497449444

x11 = -27.478935052124

x12 = 60.4856592483902

x13 = 71.4612322023811

x14 = 79.335215169929

x15 = -79.335215169929

x16 = 65.1780468952015

x17 = 33.7621203593036

x18 = -85.6184004771086

x19 = -77.7444175095607

x20 = 52.6116762808423

x21 = 96.5939734310994

x22 = 8.62937913058524

x23 = 84.0276028167403

x24 = -41.6361033268515

x25 = -40.0453056664832

x26 = -3.93699148377394

x27 = -5990.22179156555

x28 = -8.62937913058524

x29 = 27.478935052124

x30 = -21.1957497449444

x31 = 90.3107881239199

x32 = -65.1780468952015

x33 = 14.9125644377648

x34 = -2850.21993563613

x35 = 85.6184004771086

x36 = 66.7688445555698

x37 = -91.9015857842881

x38 = 29.0697327124923

x39 = -54.2024739412106

x40 = 3.93699148377394

x41 = 22.7865474053127

x42 = 40.0453056664832

x43 = -73.0520298627494

x44 = 588.273225051475

x45 = -52.6116762808423

x46 = -71.4612322023811

x47 = -66.7688445555698

x48 = -35.3529180196719

x49 = -22.7865474053127

x50 = 73.0520298627494

x51 = -58.8948615880219

x52 = 46.3284909736628

x53 = 10.2201767909535

x54 = -2.34619382340565

x55 = 91.9015857842881

x56 = -33.7621203593036

x57 = 47.919288634031

x58 = 2.34619382340565

x59 = -29.0697327124923

x60 = -60.4856592483902

x61 = 41.6361033268515

x62 = -47.919288634031

x63 = -16.5033620981331

x64 = 98.1847710914677

x65 = -90.3107881239199

x66 = -96.5939734310994

x67 = -10.2201767909535

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