sin(7x)=1 (уравнение)

Найду корень уравнения: sin(7x)=1

Вы ввели

sin(7*x) = 1

$$\sin{\left(7 x \right)} = 1$$

Подробное решение

Дано уравнение
$$\sin{\left(7 x \right)} = 1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$7 x = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$7 x = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
Или
$$7 x = 2 \pi n + \frac{\pi}{2}$$
$$7 x = 2 \pi n + \frac{\pi}{2}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$7$$
получим ответ:
$$x_{1} = \frac{2 \pi n}{7} + \frac{\pi}{14}$$
$$x_{2} = \frac{2 \pi n}{7} + \frac{\pi}{14}$$

Быстрый ответ

     pi
x1 = --
     14

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

Сумма и произведение корней

сумма

    pi
0 + --
    14

$$0 + \frac{\pi}{14}$$

=

pi
--
14

$$\frac{\pi}{14}$$

произведение

  pi
1*--
  14

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

=

pi
--
14

$$\frac{\pi}{14}$$

Численный ответ

x1 = -31.1915270456193

x2 = -27.6011355141072

x3 = 65.7490460760174

x4 = -95.8185758694717

x5 = -51.8362786970704

x6 = 98.0625705310273

x7 = 0.224399495945637

x8 = 44.2066966627658

x9 = 72.0322315039391

x10 = 42.411500768364

x11 = -85.9449991475271

x12 = 37.9235113722499

x13 = 69.3394378568687

x14 = 91.7793853552653

x15 = 78.3154168253395

x16 = 18.1763575669934

x17 = 34.3331196677168

x18 = 52.2850777114621

x19 = -34.7819186590879

x20 = -89.5353906216895

x21 = 50.4898820608836

x22 = -87.7401948323161

x23 = -25.8059396040205

x24 = -92.2281843867517

x25 = -32.0891249038338

x26 = -41.9627019386878

x27 = 81.9058085276778

x28 = 24.4595427958384

x29 = -1.57079637368157

x30 = 70.2370357653011

x31 = 96.2673748727926

x32 = -22.2155480586691

x33 = 68.441839917417

x34 = 43.3090987847674

x35 = 46.0018924252536

x36 = 62.1586547391681

x37 = -48.2458873466776

x38 = -84.1498031609459

x39 = -14.1371668789414

x40 = -53.631474642603

x41 = 2.01959524908281

x42 = -94.0233801089845

x43 = -7.8539815384555

x44 = -40.167506016662

x45 = -43.7578976689827

x46 = -69.7882367724491

x47 = 99.8577665507033

x48 = 89.984189594587

x49 = -35.6795166071758

x50 = -76.0714220599023

x51 = 26.2547386015337

x52 = -63.5050513342717

x53 = -19.5227542953327

x54 = 3.81479112194286

x55 = 88.1889938319063

x56 = -15.932362910701

x57 = -97.6137717946184

x58 = -75.1738240974786

x59 = 16.3811616358787

x60 = 86.3937979157408

x61 = 21.7667490162692

x62 = -67.9930410115775

x63 = -24.0107438405953

x64 = 11.8931722500154

x65 = 29.8451302680294

x66 = -45.5530935065707

x67 = 10.9955742763415

x68 = 63.9538504876837

x69 = 94.4721791133509

x70 = 55.875469401608

x71 = -50.0410829457155

x72 = -80.5594114848273

x73 = 73.8274274109832

x74 = 19.9715533253486

x75 = 7.40518276280084

x76 = 47.7970882498886

x77 = -66.1978451723946

x78 = -58.1194640287928

x79 = -79.6618137643714

x80 = -6.05878578546655

x81 = 60.3634587885938

x82 = 8.30278055146515

x83 = -9.64917748834828

x84 = -71.5834326602048

x85 = -17.7275585607724

x86 = -61.7098557217197

x87 = -102.101761231299

x88 = 28.0499343023253

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