cos(x)=-1/3 (уравнение)

Найду корень уравнения: cos(x)=-1/3

Вы ввели

cos(x) = -1/3

$$\cos{\left(x \right)} = - \frac{1}{3}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = - \frac{1}{3}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(- \frac{1}{3} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{1}{3} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(- \frac{1}{3} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{1}{3} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -acos(-1/3) + 2*pi

$$x_{1} = - \operatorname{acos}{\left(- \frac{1}{3} \right)} + 2 \pi$$

x2 = acos(-1/3)

$$x_{2} = \operatorname{acos}{\left(- \frac{1}{3} \right)}$$

Сумма и произведение корней

сумма

0 + -acos(-1/3) + 2*pi + acos(-1/3)

$$\operatorname{acos}{\left(- \frac{1}{3} \right)} + \left(0 + \left(- \operatorname{acos}{\left(- \frac{1}{3} \right)} + 2 \pi\right)\right)$$

=

2*pi

$$2 \pi$$

произведение

1*(-acos(-1/3) + 2*pi)*acos(-1/3)

$$1 \left(- \operatorname{acos}{\left(- \frac{1}{3} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{1}{3} \right)}$$

=

(-acos(-1/3) + 2*pi)*acos(-1/3)

$$\left(- \operatorname{acos}{\left(- \frac{1}{3} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{1}{3} \right)}$$

Численный ответ

x1 = -10.6557373781102

x2 = 39.6097450793265

x3 = 83.5920422295836

x4 = 27.0433744649674

x5 = -58.4593010008653

x6 = 4.37255207093057

x7 = -89.8752275367632

x8 = -67.2044051427264

x9 = 71.0256716152245

x10 = -14.4770038506082

x11 = -73.487590449906

x12 = 29.5052932996489

x13 = 98.6203316786244

x14 = -27.0433744649674

x15 = 77.3088569224041

x16 = 92.3371463714448

x17 = -64.7424863080449

x18 = 10.6557373781102

x19 = 35.7884786068285

x20 = 16.9389226852897

x21 = -33.326559772147

x22 = -98.6203316786244

x23 = 60.9212198355468

x24 = -8.19381854342861

x25 = 67.2044051427264

x26 = 79.7707757570856

x27 = 33.326559772147

x28 = 52.1761156936857

x29 = -60.9212198355468

x30 = 45.8929303865061

x31 = -71.0256716152245

x32 = -77.3088569224041

x33 = -971.983089376587

x34 = 48.3548492211877

x35 = 64.7424863080449

x36 = 20.7601891577878

x37 = -96.1584128439428

x38 = -23.2221079924693

x39 = 3328.17757956893

x40 = -42.0716639140081

x41 = -54.6380345283673

x42 = -29.5052932996489

x43 = -52.1761156936857

x44 = -79.7707757570856

x45 = -1.91063323624902

x46 = 1.91063323624902

x47 = 14.4770038506082

x48 = -35.7884786068285

x49 = -86.0539610642652

x50 = 86.0539610642652

x51 = 73.487590449906

x52 = 54.6380345283673

x53 = 96.1584128439428

x54 = -45.8929303865061

x55 = -39.6097450793265

x56 = -92.3371463714448

x57 = -48.3548492211877

x58 = -20.7601891577878

x59 = 8.19381854342861

x60 = -83.5920422295836

x61 = 23.2221079924693

x62 = 42.0716639140081

x63 = -4.37255207093057

x64 = 155.168999443241

x65 = 58.4593010008653

x66 = -16.9389226852897

x67 = 89.8752275367632

График