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 = -359.188760060433

x2 = -19.8967534727354

x3 = 24.0855436775217

x4 = 89.0117918517108

x5 = 17.8023583703422

x6 = 5.23598775598299

x7 = 61.7846555205993

x8 = 82.7286065445312

x9 = -80.634211442138

x10 = -5.23598775598299

x11 = 51.3126800086333

x12 = 26.1799387799149

x13 = 19.8967534727354

x14 = -26.1799387799149

x15 = -61.7846555205993

x16 = -89.0117918517108

x17 = -63.8790506229925

x18 = -11.5191730631626

x19 = -74.3510261349584

x20 = -24.0855436775217

x21 = 1651.43053823704

x22 = 11.5191730631626

x23 = -45.0294947014537

x24 = -36.6519142918809

x25 = 13.6135681655558

x26 = 99.4837673636768

x27 = -76.4454212373516

x28 = -225.147473507269

x29 = -13.6135681655558

x30 = -30.3687289847013

x31 = -32.4631240870945

x32 = 76.4454212373516

x33 = -99.4837673636768

x34 = 57.5958653158129

x35 = -68.0678408277789

x36 = 68.0678408277789

x37 = 93.2005820564972

x38 = -55.5014702134197

x39 = 70.162235930172

x40 = -1.0471975511966

x41 = -42.9350995990605

x42 = -49.2182849062401

x43 = -17.8023583703422

x44 = 32.4631240870945

x45 = 45.0294947014537

x46 = -86.9173967493176

x47 = -7.33038285837618

x48 = -70.162235930172

x49 = -51.3126800086333

x50 = 30.3687289847013

x51 = 80.634211442138

x52 = 95.2949771588904

x53 = -95.2949771588904

x54 = 36.6519142918809

x55 = 63.8790506229925

x56 = 7.33038285837618

x57 = 38.7463093942741

x58 = 1.0471975511966

x59 = 55.5014702134197

x60 = 86.9173967493176

x61 = -82.7286065445312

x62 = 49.2182849062401

x63 = -38.7463093942741

x64 = -93.2005820564972

x65 = 74.3510261349584

x66 = 42.9350995990605

x67 = -57.5958653158129

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