cos(x/3 + x) = 0 (уравнение)

Найду корень уравнения: cos(x/3 + x) = 0

Вы ввели

   /x    \    
cos|- + x| = 0
   \3    /    

$$\cos{\left(\frac{x}{3} + x \right)} = 0$$

Подробное решение

Дано уравнение
$$\cos{\left(\frac{x}{3} + x \right)} = 0$$
- это простейшее тригонометрическое ур-ние

с изменением знака при 0

Получим:
$$\cos{\left(\frac{x}{3} + x \right)} = 0$$
Это ур-ние преобразуется в
$$\frac{4 x}{3} = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$\frac{4 x}{3} = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Или
$$\frac{4 x}{3} = \pi n + \frac{\pi}{2}$$
$$\frac{4 x}{3} = \pi n - \frac{\pi}{2}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$\frac{4}{3}$$
получим ответ:
$$x_{1} = \frac{3 \pi n}{4} + \frac{3 \pi}{8}$$
$$x_{2} = \frac{3 \pi n}{4} - \frac{3 \pi}{8}$$

Быстрый ответ

     3*pi
x1 = ----
      8  

$$x_{1} = \frac{3 \pi}{8}$$

     9*pi
x2 = ----
      8  

$$x_{2} = \frac{9 \pi}{8}$$

Численный ответ

x1 = -48.3019870489431

x2 = 48.3019870489431

x3 = 93.0696823625976

x4 = 8.24668071567321

x5 = -88.3572933822129

x6 = -12.9590696960579

x7 = 64.7953484802895

x8 = -3.53429173528852

x9 = -81.2887099116359

x10 = -22.3838476568273

x11 = 74.2201264410589

x12 = 5.89048622548086

x13 = -78.9325154214436

x14 = 53.0143760293278

x15 = -57.7267650097125

x16 = 100.138265833175

x17 = 86.0010988920206

x18 = -31.8086256175967

x19 = -27.096236637212

x20 = 1928.54519022243

x21 = 22.3838476568273

x22 = 41.233403578366

x23 = 57.7267650097125

x24 = -62.4391539900971

x25 = -15.3152641862502

x26 = 88.3572933822129

x27 = -50.6581815391354

x28 = 34.164820107789

x29 = -76.5763209312512

x30 = 36.5210145979813

x31 = 1.17809724509617

x32 = -36.5210145979813

x33 = -8.24668071567321

x34 = 15.3152641862502

x35 = -253.290907695677

x36 = -45.9457925587507

x37 = 95.42587685279

x38 = -41.233403578366

x39 = 50.6581815391354

x40 = -69.5077374606742

x41 = 76.5763209312512

x42 = -74.2201264410589

x43 = -95.42587685279

x44 = -29.4524311274043

x45 = -97.7820713429823

x46 = -10.6028752058656

x47 = 20.0276531666349

x48 = 17.6714586764426

x49 = -64.7953484802895

x50 = -71.8639319508665

x51 = -225.016573813369

x52 = -20.0276531666349

x53 = 69.5077374606742

x54 = 71.8639319508665

x55 = 78.9325154214436

x56 = 62.4391539900971

x57 = 38.8772090881737

x58 = 60.0829594999048

x59 = 83.6449044018282

x60 = 55.3705705195201

x61 = 97.7820713429823

x62 = -55.3705705195201

x63 = -90.7134878724053

x64 = 43.5895980685584

x65 = 3.53429173528852

x66 = -1.17809724509617

x67 = -93.0696823625976

x68 = 12.9590696960579

x69 = -43.5895980685584

x70 = -86.0010988920206

x71 = -100.138265833175

x72 = -67.1515429704818

x73 = 102.494460323367

x74 = 31.8086256175967

x75 = 90.7134878724053

x76 = -60.0829594999048

x77 = 45.9457925587507

x78 = -17.6714586764426

x79 = 24.7400421470196

x80 = -5.89048622548086

x81 = -53.0143760293278

x82 = 81.2887099116359

x83 = 29.4524311274043

x84 = 10.6028752058656

x85 = -83.6449044018282

x86 = -34.164820107789

x87 = -24.7400421470196

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