cos(3x/2)=0 (уравнение)

Найду корень уравнения: cos(3x/2)=0

Вы ввели

   /3*x\    
cos|---| = 0
   \ 2 /    

$$\cos{\left(\frac{3 x}{2} \right)} = 0$$

Подробное решение

Дано уравнение
$$\cos{\left(\frac{3 x}{2} \right)} = 0$$
- это простейшее тригонометрическое ур-ние

с изменением знака при 0

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

Быстрый ответ

     pi
x1 = --
     3 

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

x2 = pi

$$x_{2} = \pi$$

Сумма и произведение корней

сумма

    pi     
0 + -- + pi
    3      

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

=

4*pi
----
 3  

$$\frac{4 \pi}{3}$$

произведение

  pi   
1*--*pi
  3    

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

=

  2
pi 
---
 3 

$$\frac{\pi^{2}}{3}$$

Численный ответ

x1 = -505.796417227957

x2 = 59.6902604182061

x3 = 40.8407044966673

x4 = 74.3510261349584

x5 = 21.9911485751286

x6 = 82.7286065445312

x7 = -55.5014702134197

x8 = 38.7463093942741

x9 = 95.2949771588904

x10 = 7180.63360855507

x11 = 13.6135681655558

x12 = -99.4837673636768

x13 = 42.9350995990605

x14 = 26.1799387799149

x15 = -5.23598775598299

x16 = -76.4454212373516

x17 = -32.4631240870945

x18 = 97.3893722612836

x19 = 68.0678408277789

x20 = -30.3687289847013

x21 = 99.4837673636768

x22 = 72.2566310325652

x23 = -51.3126800086333

x24 = 3.14159265358979

x25 = -80.634211442138

x26 = -53.4070751110265

x27 = -72.2566310325652

x28 = -47.1238898038469

x29 = -34.5575191894877

x30 = 7.33038285837618

x31 = -26.1799387799149

x32 = -21.9911485751286

x33 = 91.106186954104

x34 = 47.1238898038469

x35 = -3.14159265358979

x36 = -49.2182849062401

x37 = 55.5014702134197

x38 = -78.5398163397448

x39 = 34.5575191894877

x40 = -74.3510261349584

x41 = -63.8790506229925

x42 = 86.9173967493176

x43 = -24.0855436775217

x44 = 80.634211442138

x45 = -97.3893722612836

x46 = 15.707963267949

x47 = 9.42477796076938

x48 = 63.8790506229925

x49 = 24.0855436775217

x50 = 51.3126800086333

x51 = -7.33038285837618

x52 = -13.6135681655558

x53 = 19.8967534727354

x54 = 61.7846555205993

x55 = -36.6519142918809

x56 = 65.9734457253857

x57 = -61.7846555205993

x58 = 17.8023583703422

x59 = -82.7286065445312

x60 = -19.8967534727354

x61 = 28.2743338823081

x62 = -45.0294947014537

x63 = 70.162235930172

x64 = 76.4454212373516

x65 = -70.162235930172

x66 = -57.5958653158129

x67 = -1.0471975511966

x68 = -91.106186954104

x69 = -11.5191730631626

x70 = 32.4631240870945

x71 = 122.522113490002

x72 = -28.2743338823081

x73 = -17.8023583703422

x74 = 57.5958653158129

x75 = -68.0678408277789

x76 = -59.6902604182061

x77 = -95.2949771588904

x78 = -9.42477796076938

x79 = -15.707963267949

x80 = 30.3687289847013

x81 = 78.5398163397448

x82 = 11.5191730631626

x83 = 84.8230016469244

x84 = -93.2005820564972

x85 = -65.9734457253857

x86 = 36.6519142918809

x87 = 53.4070751110265

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