cos(x)=-1/6 (уравнение)

Найду корень уравнения: cos(x)=-1/6

Вы ввели

cos(x) = -1/6

$$\cos{\left(x \right)} = - \frac{1}{6}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = - \frac{1}{6}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(- \frac{1}{6} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{1}{6} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(- \frac{1}{6} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{1}{6} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -acos(-1/6) + 2*pi

$$x_{1} = - \operatorname{acos}{\left(- \frac{1}{6} \right)} + 2 \pi$$

x2 = acos(-1/6)

$$x_{2} = \operatorname{acos}{\left(- \frac{1}{6} \right)}$$

Сумма и произведение корней

сумма

0 + -acos(-1/6) + 2*pi + acos(-1/6)

$$\operatorname{acos}{\left(- \frac{1}{6} \right)} + \left(0 + \left(- \operatorname{acos}{\left(- \frac{1}{6} \right)} + 2 \pi\right)\right)$$

=

2*pi

$$2 \pi$$

произведение

1*(-acos(-1/6) + 2*pi)*acos(-1/6)

$$1 \left(- \operatorname{acos}{\left(- \frac{1}{6} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{1}{6} \right)}$$

=

(-acos(-1/6) + 2*pi)*acos(-1/6)

$$\left(- \operatorname{acos}{\left(- \frac{1}{6} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{1}{6} \right)}$$

Численный ответ

x1 = -83.4196533993492

x2 = -89.7028387065288

x3 = 8.02142971319417

x4 = 54.8104233586017

x5 = 92.5095352016792

x6 = 52.0037268634513

x7 = 77.1364680921696

x8 = 83.4196533993492

x9 = -95.9860240137084

x10 = -54.8104233586017

x11 = 86.2263498944996

x12 = -10.8281262083446

x13 = -61.0936086657813

x14 = 89.7028387065288

x15 = -67.3767939729609

x16 = -92.5095352016792

x17 = -98.7927205088588

x18 = 48.5272380514221

x19 = -33.1541709419125

x20 = 4.544940901165

x21 = 45.7205415562717

x22 = 23.3944968227038

x23 = 29.6776821298833

x24 = -17.1113115155242

x25 = -70.85328278499

x26 = -64.5700974778104

x27 = 61.0936086657813

x28 = -29.6776821298833

x29 = -4.544940901165

x30 = -20.5878003275533

x31 = 73.6599792801404

x32 = 64.5700974778104

x33 = 33.1541709419125

x34 = -77.1364680921696

x35 = -1.73824440601459

x36 = 14.3046150203738

x37 = 35.9608674370629

x38 = -73.6599792801404

x39 = -86.2263498944996

x40 = 98.7927205088588

x41 = 70.85328278499

x42 = 95.9860240137084

x43 = 26.8709856347329

x44 = -52.0037268634513

x45 = -79.94316458732

x46 = -48.5272380514221

x47 = -8.02142971319417

x48 = 79.94316458732

x49 = -35.9608674370629

x50 = 42.2440527442425

x51 = 67.3767939729609

x52 = -45.7205415562717

x53 = -14.3046150203738

x54 = -58.2869121706309

x55 = -39.4373562490921

x56 = -23.3944968227038

x57 = -26.8709856347329

x58 = 1.73824440601459

x59 = 58.2869121706309

x60 = 39.4373562490921

x61 = 102.269209320888

x62 = 10.8281262083446

x63 = 17.1113115155242

x64 = 20.5878003275533

x65 = -42.2440527442425

График