cos(7*x)=0 (уравнение)

Найду корень уравнения: cos(7*x)=0

Вы ввели

cos(7*x) = 0

$$\cos{\left(7 x \right)} = 0$$

Подробное решение

Дано уравнение
$$\cos{\left(7 x \right)} = 0$$
- это простейшее тригонометрическое ур-ние

с изменением знака при 0

Получим:
$$\cos{\left(7 x \right)} = 0$$
Это ур-ние преобразуется в
$$7 x = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$7 x = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Или
$$7 x = \pi n + \frac{\pi}{2}$$
$$7 x = \pi n - \frac{\pi}{2}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$7$$
получим ответ:
$$x_{1} = \frac{\pi n}{7} + \frac{\pi}{14}$$
$$x_{2} = \frac{\pi n}{7} - \frac{\pi}{14}$$

Быстрый ответ

     pi
x1 = --
     14

$$x_{1} = \frac{\pi}{14}$$

     3*pi
x2 = ----
      14 

$$x_{2} = \frac{3 \pi}{14}$$

Сумма и произведение корней

сумма

    pi   3*pi
0 + -- + ----
    14    14 

$$\left(0 + \frac{\pi}{14}\right) + \frac{3 \pi}{14}$$

=

2*pi
----
 7  

$$\frac{2 \pi}{7}$$

произведение

  pi 3*pi
1*--*----
  14  14 

$$\frac{3 \pi}{14} \cdot 1 \frac{\pi}{14}$$

=

    2
3*pi 
-----
 196 

$$\frac{3 \pi^{2}}{196}$$

Численный ответ

x1 = 36.1283155162826

x2 = 8.30278058448731

x3 = 78.3154168644884

x4 = 76.0714221119243

x5 = -33.8843207637185

x6 = -43.7578976750007

x7 = 19.9715532978208

x8 = 100.306565439617

x9 = -69.7882368047447

x10 = 40.1675060708981

x11 = -59.9146598934625

x12 = -76.0714221119243

x13 = 37.4747123678211

x14 = -91.7793853798732

x15 = 26.2547386050004

x16 = 0.224399475256414

x17 = 3.81479107935903

x18 = -95.8185759344887

x19 = -72.0322315573088

x20 = -50.0410829821803

x21 = -85.9449990232065

x22 = 58.1194640914112

x23 = -28.0499344070517

x24 = -3.81479107935903

x25 = 88.1889937757706

x26 = 14.1371669411541

x27 = -41.9627018729494

x28 = 28.0499344070517

x29 = -46.0018924275648

x30 = 22.215548050385

x31 = -98.0625706870528

x32 = -94.0233801324374

x33 = 85.9449990232065

x34 = -7.85398163397448

x35 = -21.7667490998721

x36 = -19.9715532978208

x37 = 92.2281843303861

x38 = 2.01959527730772

x39 = -32.53792391218

x40 = 74.276226309873

x41 = 10.0979763865386

x42 = -15.9323627432054

x43 = 41.9627018729494

x44 = -65.7490462501292

x45 = 98.0625706870528

x46 = -83.7010042706423

x47 = -87.7401948252578

x48 = -24.0107438524363

x49 = -2.01959527730772

x50 = 96.2673748850015

x51 = 52.2850777347444

x52 = 32.0891249616672

x53 = -37.9235113183339

x54 = 4.26359002987186

x55 = -89.9841895778219

x56 = -61.7098556955138

x57 = 63.9538504480779

x58 = 94.0233801324374

x59 = -80.5594116170526

x60 = -17.7275585452567

x61 = -11.8931721885899

x62 = 15.9323627432054

x63 = -67.9930410026934

x64 = -29.845130209103

x65 = 66.1978452006421

x66 = 18.1763574957695

x67 = 46.0018924275648

x68 = -47.7970882296161

x69 = -6.05878583192317

x70 = 6.05878583192317

x71 = 44.2066966255135

x72 = 54.0802735367957

x73 = 50.0410829821803

x74 = 89.9841895778219

x75 = 70.2370357552575

x76 = 84.1498032211552

x77 = -55.875469338847

x78 = 67.9930410026934

x79 = -73.8274273593601

x80 = 62.1586546460266

x81 = -35.6795165657698

x82 = 24.0107438524363

x83 = -99.8577664891041

x84 = -81.905808468591

x85 = -51.8362787842316

x86 = 80.1106126665397

x87 = 72.0322315573088

x88 = -39.7187071203852

x89 = 30.2939291596159

x90 = -25.8059396544876

x91 = -77.8666179139756

x92 = 56.7730672398727

x93 = -63.9538504480779

x94 = 48.245887180129

x95 = -13.6883679906412

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