1/3=cos(x) (уравнение)

Найду корень уравнения: 1/3=cos(x)

Вы ввели

1/3 = cos(x)

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

Подробное решение

Дано уравнение
$$\frac{1}{3} = \cos{\left(x \right)}$$
- это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на -1

Ур-ние превратится в
$$\cos{\left(x \right)} = \frac{1}{3}$$
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 = -51.4964418747775

x2 = -99.3000054975326

x3 = 1.23095941734077

x4 = 23.9017818113776

x5 = -55.3177083472755

x6 = -32.6468859532387

x7 = -42.7513377329163

x8 = -26.3637006460591

x9 = 11.3354111970184

x10 = -101.761924332214

x11 = -45.2132565675979

x12 = 70.3459977963162

x13 = -38.9300712604183

x14 = -74.1672642688143

x15 = 20.0805153388795

x16 = 49.0345230400959

x17 = -86.7336348831734

x18 = 99.3000054975326

x19 = 42.7513377329163

x20 = -13.7973300316999

x21 = -11.3354111970184

x22 = -80.4504495759938

x23 = -64.0628124891366

x24 = 82.9123684106754

x25 = -36.4681524257367

x26 = 38.9300712604183

x27 = -93.016820190353

x28 = 67.8840789616347

x29 = -57.7796271819571

x30 = -325.494676555998

x31 = 26.3637006460591

x32 = -82.9123684106754

x33 = -89.195553717855

x34 = 51.4964418747775

x35 = 55.3177083472755

x36 = -5.05222588983881

x37 = 7.51414472452036

x38 = -7.51414472452036

x39 = 17.618596504198

x40 = 64.0628124891366

x41 = 76.6291831034958

x42 = 95.4787390250346

x43 = -67.8840789616347

x44 = 13.7973300316999

x45 = -61.6008936544551

x46 = 80.4504495759938

x47 = 74.1672642688143

x48 = 30.1849671185572

x49 = -70.3459977963162

x50 = 45.2132565675979

x51 = 57.7796271819571

x52 = 36.4681524257367

x53 = 89.195553717855

x54 = -95.4787390250346

x55 = 93.016820190353

x56 = -30.1849671185572

x57 = 86.7336348831734

x58 = -17.618596504198

x59 = 32.6468859532387

x60 = -23.9017818113776

x61 = -49.0345230400959

x62 = 5.05222588983881

x63 = -1.23095941734077

x64 = -76.6291831034958

x65 = 61.6008936544551

x66 = -20.0805153388795

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