cos(4*x)=0 (уравнение)

Найду корень уравнения: cos(4*x)=0

Вы ввели

cos(4*x) = 0

$$\cos{\left(4 x \right)} = 0$$

Подробное решение

Дано уравнение
$$\cos{\left(4 x \right)} = 0$$
- это простейшее тригонометрическое ур-ние

с изменением знака при 0

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

Быстрый ответ

     pi
x1 = --
     8 

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

     3*pi
x2 = ----
      8  

$$x_{2} = \frac{3 \pi}{8}$$

Сумма и произведение корней

сумма

    pi   3*pi
0 + -- + ----
    8     8  

$$\left(0 + \frac{\pi}{8}\right) + \frac{3 \pi}{8}$$

=

pi
--
2 

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

произведение

  pi 3*pi
1*--*----
  8   8  

$$\frac{3 \pi}{8} \cdot 1 \frac{\pi}{8}$$

=

    2
3*pi 
-----
  64 

$$\frac{3 \pi^{2}}{64}$$

Численный ответ

x1 = -39.6626072515711

x2 = 4.31968989868597

x3 = -64.009950316892

x4 = -79.717913584841

x5 = -12.1736715326604

x6 = 71.8639319508665

x7 = 56.1559686829176

x8 = -56.1559686829176

x9 = -86.0010988920206

x10 = -17.6714586764426

x11 = 67.9369411338793

x12 = 96.9966731795849

x13 = 45.9457925587507

x14 = -65.5807466436869

x15 = 12.1736715326604

x16 = -31.8086256175967

x17 = -21.5984494934298

x18 = -68.7223392972767

x19 = 20.0276531666349

x20 = 89.9280897090078

x21 = -16.1006623496477

x22 = -61.6537558266997

x23 = 38.0918109247762

x24 = 53.7997741927252

x25 = 100.138265833175

x26 = 48.3019870489431

x27 = 92.2842841992002

x28 = 26.3108384738145

x29 = -42.0188017417635

x30 = 62.4391539900971

x31 = 82.0741080750334

x32 = 42.0188017417635

x33 = 34.164820107789

x34 = 60.0829594999048

x35 = -5.89048622548086

x36 = 52.2289778659303

x37 = 49.872783375738

x38 = 66.3661448070844

x39 = -13.7444678594553

x40 = -2.74889357189107

x41 = -20.0276531666349

x42 = 23.9546439836222

x43 = -27.8816348006094

x44 = 64.009950316892

x45 = -23.9546439836222

x46 = -78.1471172580461

x47 = -82.0741080750334

x48 = -49.872783375738

x49 = 22.3838476568273

x50 = 104.850654813559

x51 = 27.8816348006094

x52 = -35.7356164345839

x53 = 84.4303025652257

x54 = 0.392699081698724

x55 = -38.0918109247762

x56 = 122.914812571701

x57 = 30.2378292908018

x58 = 54.5851723561227

x59 = 5.89048622548086

x60 = 78.1471172580461

x61 = -43.5895980685584

x62 = 16.1006623496477

x63 = -83.6449044018282

x64 = -87.5718952188155

x65 = 93.8550805259951

x66 = 1.96349540849362

x67 = -89.9280897090078

x68 = 86.0010988920206

x69 = -67.9369411338793

x70 = 9.8174770424681

x71 = 96.2112750161874

x72 = -10.6028752058656

x73 = 88.3572933822129

x74 = -60.0829594999048

x75 = 70.2931356240716

x76 = 8.24668071567321

x77 = -75.7909227678538

x78 = -75.0055246044563

x79 = -9.8174770424681

x80 = -1.96349540849362

x81 = -57.7267650097125

x82 = -71.8639319508665

x83 = 31.8086256175967

x84 = 44.3749962319558

x85 = -93.8550805259951

x86 = -20.8130513300324

x87 = -45.9457925587507

x88 = -96.9966731795849

x89 = -97.7820713429823

x90 = 74.2201264410589

x91 = 40.4480054149686

x92 = -34.164820107789

x93 = -53.7997741927252

x94 = -100.138265833175

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