cos(x)=0.5 (уравнение)

Найду корень уравнения: cos(x)=0.5

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
0 + -- + ----
    3     3  

$$\left(0 + \frac{\pi}{3}\right) + \frac{5 \pi}{3}$$

=

2*pi

$$2 \pi$$

произведение

  pi 5*pi
1*--*----
  3   3  

$$\frac{5 \pi}{3} \cdot 1 \frac{\pi}{3}$$

=

    2
5*pi 
-----
  9  

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

Численный ответ

x1 = -63.8790506229925

x2 = 57.5958653158129

x3 = 63.8790506229925

x4 = 49.2182849062401

x5 = 74.3510261349584

x6 = 51.3126800086333

x7 = -45.0294947014537

x8 = -17.8023583703422

x9 = -5.23598775598299

x10 = -24.0855436775217

x11 = 1651.43053823704

x12 = -95.2949771588904

x13 = -89.0117918517108

x14 = 70.162235930172

x15 = -30.3687289847013

x16 = -359.188760060433

x17 = 32.4631240870945

x18 = -38.7463093942741

x19 = 93.2005820564972

x20 = 5.23598775598299

x21 = 61.7846555205993

x22 = -68.0678408277789

x23 = 45.0294947014537

x24 = 80.634211442138

x25 = 1.0471975511966

x26 = 24.0855436775217

x27 = 19.8967534727354

x28 = -11.5191730631626

x29 = 11.5191730631626

x30 = 86.9173967493176

x31 = -61.7846555205993

x32 = 99.4837673636768

x33 = -51.3126800086333

x34 = 82.7286065445312

x35 = -1.0471975511966

x36 = -76.4454212373516

x37 = -7.33038285837618

x38 = 17.8023583703422

x39 = 89.0117918517108

x40 = -13.6135681655558

x41 = 68.0678408277789

x42 = -99.4837673636768

x43 = -80.634211442138

x44 = -19.8967534727354

x45 = 36.6519142918809

x46 = 7.33038285837618

x47 = 76.4454212373516

x48 = -55.5014702134197

x49 = -36.6519142918809

x50 = -225.147473507269

x51 = -57.5958653158129

x52 = -32.4631240870945

x53 = -82.7286065445312

x54 = -42.9350995990605

x55 = 38.7463093942741

x56 = 30.3687289847013

x57 = 55.5014702134197

x58 = 26.1799387799149

x59 = -93.2005820564972

x60 = -70.162235930172

x61 = -74.3510261349584

x62 = 42.9350995990605

x63 = -86.9173967493176

x64 = 95.2949771588904

x65 = 13.6135681655558

x66 = -49.2182849062401

x67 = -26.1799387799149

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