cos(5x)=0 (уравнение)

Найду корень уравнения: cos(5x)=0

Вы ввели

cos(5*x) = 0

$$\cos{\left(5 x \right)} = 0$$

Подробное решение

Дано уравнение
$$\cos{\left(5 x \right)} = 0$$
- это простейшее тригонометрическое ур-ние

с изменением знака при 0

Получим:
$$\cos{\left(5 x \right)} = 0$$
Это ур-ние преобразуется в
$$5 x = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$5 x = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Или
$$5 x = \pi n + \frac{\pi}{2}$$
$$5 x = \pi n - \frac{\pi}{2}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$5$$
получим ответ:
$$x_{1} = \frac{\pi n}{5} + \frac{\pi}{10}$$
$$x_{2} = \frac{\pi n}{5} - \frac{\pi}{10}$$

Быстрый ответ

     pi
x1 = --
     10

$$x_{1} = \frac{\pi}{10}$$

     3*pi
x2 = ----
      10 

$$x_{2} = \frac{3 \pi}{10}$$

Сумма и произведение корней

сумма

    pi   3*pi
0 + -- + ----
    10    10 

$$\left(0 + \frac{\pi}{10}\right) + \frac{3 \pi}{10}$$

=

2*pi
----
 5  

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

произведение

  pi 3*pi
1*--*----
  10  10 

$$\frac{3 \pi}{10} \cdot 1 \frac{\pi}{10}$$

=

    2
3*pi 
-----
 100 

$$\frac{3 \pi^{2}}{100}$$

Численный ответ

x1 = 17.9070781254618

x2 = 65.0309679293087

x3 = 36.1283155162826

x4 = -65.6592864600267

x5 = -76.9690200129499

x6 = 61.8893752757189

x7 = 48.0663675999238

x8 = -71.9424717672063

x9 = 46.18141200777

x10 = 98.3318500573605

x11 = 27.3318560862312

x12 = -14.1371669411541

x13 = -16.0221225333079

x14 = -53.0929158456675

x15 = 60.0044196835651

x16 = -9.73893722612836

x17 = 95.1902574037707

x18 = 56.2345084992573

x19 = -95.8185759344887

x20 = 32.3584043319749

x21 = 58.1194640914112

x22 = 10.3672557568463

x23 = 22.3053078404875

x24 = 14.1371669411541

x25 = -61.8893752757189

x26 = -58.1194640914112

x27 = -33.6150413934108

x28 = -39.8982267005904

x29 = -7.85398163397448

x30 = 66.2876049907446

x31 = 92.0486647501809

x32 = 71.9424717672063

x33 = 81.9955682586936

x34 = -53.7212343763855

x35 = -48.0663675999238

x36 = 90.1637091580271

x37 = -5.96902604182061

x38 = -63.7743308678728

x39 = -80.1106126665397

x40 = 88.2787535658732

x41 = 16.0221225333079

x42 = 4.08407044966673

x43 = -27.9601746169492

x44 = 49.9513231920777

x45 = -38.0132711084365

x46 = -75.712382951514

x47 = -11.6238928182822

x48 = -19.7920337176157

x49 = -69.4291976443344

x50 = -21.6769893097696

x51 = 12.2522113490002

x52 = 93.9336203423348

x53 = 2.19911485751286

x54 = 38.0132711084365

x55 = 76.340701482232

x56 = 70.0575161750524

x57 = -83.8805238508475

x58 = 68.1725605828985

x59 = -92.0486647501809

x60 = 7.22566310325652

x61 = -49.9513231920777

x62 = -17.9070781254618

x63 = -87.6504350351552

x64 = 44.2964564156161

x65 = -29.845130209103

x66 = 88.9070720965912

x67 = 5.96902604182061

x68 = -70.0575161750524

x69 = -31.7300858012569

x70 = 27.9601746169492

x71 = -81.9955682586936

x72 = 100.216805649514

x73 = -60.0044196835651

x74 = 72.5707902979242

x75 = 26.0752190247953

x76 = -85.7654794430014

x77 = -26.0752190247953

x78 = -41.7831822927443

x79 = -73.8274273593601

x80 = 0.314159265358979

x81 = -4.08407044966673

x82 = -102.730079772386

x83 = -51.8362787842316

x84 = 80.1106126665397

x85 = 21.0486707790516

x86 = -93.9336203423348

x87 = 39.8982267005904

x88 = 54.3495529071034

x89 = 78.2256570743859

x90 = -36.1283155162826

x91 = 83.8805238508475

x92 = -97.7035315266426

x93 = 34.2433599241287

x94 = -103.358398303104

x95 = 24.1902634326414

x96 = -43.6681378848981

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