cos(x)=0,75 (уравнение)

Найду корень уравнения: cos(x)=0,75

Вы ввели

cos(x) = 3/4

$$\cos{\left(x \right)} = \frac{3}{4}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = \frac{3}{4}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(\frac{3}{4} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{3}{4} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(\frac{3}{4} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{3}{4} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -acos(3/4) + 2*pi

$$x_{1} = - \operatorname{acos}{\left(\frac{3}{4} \right)} + 2 \pi$$

x2 = acos(3/4)

$$x_{2} = \operatorname{acos}{\left(\frac{3}{4} \right)}$$

Сумма и произведение корней

сумма

0 + -acos(3/4) + 2*pi + acos(3/4)

$$\operatorname{acos}{\left(\frac{3}{4} \right)} + \left(0 + \left(- \operatorname{acos}{\left(\frac{3}{4} \right)} + 2 \pi\right)\right)$$

=

2*pi

$$2 \pi$$

произведение

1*(-acos(3/4) + 2*pi)*acos(3/4)

$$1 \left(- \operatorname{acos}{\left(\frac{3}{4} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{3}{4} \right)}$$

=

(-acos(3/4) + 2*pi)*acos(3/4)

$$\left(- \operatorname{acos}{\left(\frac{3}{4} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{3}{4} \right)}$$

Численный ответ

x1 = -74.6754894383416

x2 = -32.1386607837113

x3 = -57.2714020124297

x4 = 0.722734247813416

x5 = 99.80823066706

x6 = 69.8377726267889

x7 = 38.4218460908909

x8 = -63.5545873196093

x9 = -5.56045105936617

x10 = -50.9882167052501

x11 = -49.5427482096233

x12 = 62.1091188239824

x13 = -101.253699162687

x14 = 76.1209579339685

x15 = -62.1091188239824

x16 = 5.56045105936617

x17 = -19.5722901693522

x18 = 80.9586747455212

x19 = -13.2891048621726

x20 = 74.6754894383416

x21 = -68.392304131162

x22 = 19.5722901693522

x23 = 63.5545873196093

x24 = 420.250681333219

x25 = -7.005919554993

x26 = -11.8436363665458

x27 = 43.2595629024437

x28 = 57.2714020124297

x29 = -94.9705138555072

x30 = -36.9763775952641

x31 = 44.7050313980705

x32 = 157.802366927303

x33 = 88.6873285483276

x34 = 82.404143241148

x35 = 55.8259335168029

x36 = 18.1268216737253

x37 = 68.392304131162

x38 = 93.5250453598804

x39 = -93.5250453598804

x40 = 49.5427482096233

x41 = -0.722734247813416

x42 = -25.8554754765318

x43 = -76.1209579339685

x44 = 25.8554754765318

x45 = 36.9763775952641

x46 = -82.404143241148

x47 = -24.4100069809049

x48 = -80.9586747455212

x49 = 13.2891048621726

x50 = -38.4218460908909

x51 = 11.8436363665458

x52 = -30.6931922880845

x53 = 87.2418600527008

x54 = -43.2595629024437

x55 = 30.6931922880845

x56 = -18.1268216737253

x57 = -55.8259335168029

x58 = -99.80823066706

x59 = 32.1386607837113

x60 = 50.9882167052501

x61 = 94.9705138555072

x62 = 16770.5443191101

x63 = -44.7050313980705

x64 = 7.005919554993

x65 = 24.4100069809049

x66 = -87.2418600527008

x67 = -69.8377726267889

x68 = -88.6873285483276

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