cos(x)=0.3 (уравнение)

Найду корень уравнения: cos(x)=0.3

Вы ввели

cos(x) = 3/10

$$\cos{\left(x \right)} = \frac{3}{10}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = \frac{3}{10}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(\frac{3}{10} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{3}{10} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(\frac{3}{10} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{3}{10} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -acos(3/10) + 2*pi

$$x_{1} = - \operatorname{acos}{\left(\frac{3}{10} \right)} + 2 \pi$$

x2 = acos(3/10)

$$x_{2} = \operatorname{acos}{\left(\frac{3}{10} \right)}$$

Сумма и произведение корней

сумма

0 + -acos(3/10) + 2*pi + acos(3/10)

$$\operatorname{acos}{\left(\frac{3}{10} \right)} + \left(0 + \left(- \operatorname{acos}{\left(\frac{3}{10} \right)} + 2 \pi\right)\right)$$

=

2*pi

$$2 \pi$$

произведение

1*(-acos(3/10) + 2*pi)*acos(3/10)

$$1 \left(- \operatorname{acos}{\left(\frac{3}{10} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{3}{10} \right)}$$

=

(-acos(3/10) + 2*pi)*acos(3/10)

$$\left(- \operatorname{acos}{\left(\frac{3}{10} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{3}{10} \right)}$$

Численный ответ

x1 = -30.1498228631184

x2 = -11.3002669415797

x3 = -92.9816759349143

x4 = 17.5834522487593

x5 = 20.1156595943183

x6 = 86.6984906277347

x7 = -45.2484008230366

x8 = -1.2661036727795

x9 = -64.0979567445754

x10 = -86.6984906277347

x11 = 61.5657493990164

x12 = 38.965215515857

x13 = -74.1321200133755

x14 = -57.8147714373958

x15 = -42.7161934774776

x16 = -23.8666375559388

x17 = 82.9475126661141

x18 = -17.5834522487593

x19 = 95.5138832804733

x20 = -36.433008170298

x21 = -99.2648612420939

x22 = 26.3988449014978

x23 = 92.9816759349143

x24 = 67.8489347061959

x25 = 1.2661036727795

x26 = -95.5138832804733

x27 = -80.4153053205551

x28 = 70.3811420517549

x29 = 42.7161934774776

x30 = 32.6820302086774

x31 = -70.3811420517549

x32 = 23.8666375559388

x33 = 11.3002669415797

x34 = 57.8147714373958

x35 = 48.9993787846572

x36 = 55.2825640918368

x37 = -7.54928897995909

x38 = 64.0979567445754

x39 = -5.01708163440009

x40 = 99.2648612420939

x41 = 89.2306979732937

x42 = 30.1498228631184

x43 = 36.433008170298

x44 = 80.4153053205551

x45 = -89.2306979732937

x46 = -51.5315861302162

x47 = -55.2825640918368

x48 = 45.2484008230366

x49 = -32.6820302086774

x50 = 7.54928897995909

x51 = -20.1156595943183

x52 = 76.6643273589345

x53 = -61.5657493990164

x54 = -67.8489347061959

x55 = -76.6643273589345

x56 = -38.965215515857

x57 = 74.1321200133755

x58 = -48.9993787846572

x59 = 5.01708163440009

x60 = -82.9475126661141

x61 = -26.3988449014978

x62 = 13.8324742871387

x63 = 51.5315861302162

x64 = -13.8324742871387

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