cos(x)=1/2 (уравнение)

Найду корень уравнения: cos(x)=1/2

Вы ввели

cos(x) = 1/2

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

Подробное решение

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

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

Сумма и произведение корней

сумма

pi   5*pi
-- + ----
3     3  

$$\frac{\pi}{3} + \frac{5 \pi}{3}$$

=

2*pi

$$2 \pi$$

произведение

pi 5*pi
--*----
3   3  

$$\frac{\pi}{3} \frac{5 \pi}{3}$$

=

    2
5*pi 
-----
  9  

$$\frac{5 \pi^{2}}{9}$$

Численный ответ

x1 = 55.5014702134197

x2 = -93.2005820564972

x3 = 26.1799387799149

x4 = 42.9350995990605

x5 = -7.33038285837618

x6 = -17.8023583703422

x7 = -359.188760060433

x8 = 5.23598775598299

x9 = 70.162235930172

x10 = 11.5191730631626

x11 = -49.2182849062401

x12 = -76.4454212373516

x13 = 74.3510261349584

x14 = -19.8967534727354

x15 = 89.0117918517108

x16 = 32.4631240870945

x17 = -74.3510261349584

x18 = 93.2005820564972

x19 = 86.9173967493176

x20 = 76.4454212373516

x21 = -82.7286065445312

x22 = 36.6519142918809

x23 = 82.7286065445312

x24 = 38.7463093942741

x25 = -42.9350995990605

x26 = -24.0855436775217

x27 = -36.6519142918809

x28 = 30.3687289847013

x29 = -68.0678408277789

x30 = 24.0855436775217

x31 = -99.4837673636768

x32 = 61.7846555205993

x33 = -45.0294947014537

x34 = -57.5958653158129

x35 = -63.8790506229925

x36 = -26.1799387799149

x37 = -95.2949771588904

x38 = -86.9173967493176

x39 = 99.4837673636768

x40 = 45.0294947014537

x41 = -13.6135681655558

x42 = 63.8790506229925

x43 = -32.4631240870945

x44 = 68.0678408277789

x45 = 13.6135681655558

x46 = 51.3126800086333

x47 = -70.162235930172

x48 = -89.0117918517108

x49 = -5.23598775598299

x50 = 19.8967534727354

x51 = -225.147473507269

x52 = -38.7463093942741

x53 = -1.0471975511966

x54 = 1.0471975511966

x55 = -51.3126800086333

x56 = -80.634211442138

x57 = 7.33038285837618

x58 = 49.2182849062401

x59 = -61.7846555205993

x60 = 1651.43053823704

x61 = -55.5014702134197

x62 = -30.3687289847013

x63 = -11.5191730631626

x64 = 80.634211442138

x65 = 17.8023583703422

x66 = 95.2949771588904

x67 = 57.5958653158129

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