2cos(x)=1 (уравнение)

Найду корень уравнения: 2cos(x)=1

Вы ввели

2*cos(x) = 1

$$2 \cos{\left(x \right)} = 1$$

Подробное решение

Дано уравнение
$$2 \cos{\left(x \right)} = 1$$
- это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на 2

Ур-ние превратится в
$$\cos{\left(x \right)} = \frac{1}{2}$$
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
Или
$$x = \pi n + \frac{\pi}{3}$$
$$x = \pi n - \frac{2 \pi}{3}$$
, где n - любое целое число

Быстрый ответ

     pi
x1 = --
     3 

$$x_{1} = \frac{\pi}{3}$$

     5*pi
x2 = ----
      3  

$$x_{2} = \frac{5 \pi}{3}$$

Численный ответ

x1 = -63.8790506229925

x2 = -17.8023583703422

x3 = 7.33038285837618

x4 = 93.2005820564972

x5 = -30.3687289847013

x6 = -93.2005820564972

x7 = 32.4631240870945

x8 = -51.3126800086333

x9 = 11.5191730631626

x10 = 49.2182849062401

x11 = -70.162235930172

x12 = 38.7463093942741

x13 = -32.4631240870945

x14 = 95.2949771588904

x15 = 13.6135681655558

x16 = -38.7463093942741

x17 = -55.5014702134197

x18 = 74.3510261349584

x19 = 89.0117918517108

x20 = 80.634211442138

x21 = 1.0471975511966

x22 = 63.8790506229925

x23 = -19.8967534727354

x24 = -68.0678408277789

x25 = 61.7846555205993

x26 = 26.1799387799149

x27 = -95.2949771588904

x28 = -359.188760060433

x29 = -57.5958653158129

x30 = 68.0678408277789

x31 = 19.8967534727354

x32 = -11.5191730631626

x33 = -5.23598775598299

x34 = -36.6519142918809

x35 = 17.8023583703422

x36 = 86.9173967493176

x37 = 30.3687289847013

x38 = -26.1799387799149

x39 = 42.9350995990605

x40 = -1.0471975511966

x41 = 45.0294947014537

x42 = -89.0117918517108

x43 = -99.4837673636768

x44 = 70.162235930172

x45 = 55.5014702134197

x46 = -42.9350995990605

x47 = -49.2182849062401

x48 = 99.4837673636768

x49 = 36.6519142918809

x50 = -45.0294947014537

x51 = -13.6135681655558

x52 = -80.634211442138

x53 = 1651.43053823704

x54 = -76.4454212373516

x55 = -24.0855436775217

x56 = -74.3510261349584

x57 = -61.7846555205993

x58 = 57.5958653158129

x59 = -82.7286065445312

x60 = 51.3126800086333

x61 = -86.9173967493176

x62 = 5.23598775598299

x63 = -7.33038285837618

x64 = 24.0855436775217

x65 = 82.7286065445312

x66 = 76.4454212373516

x67 = -225.147473507269

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