sin(x)=-1/5 (уравнение)

Найду корень уравнения: sin(x)=-1/5

Вы ввели

sin(x) = -1/5

$$\sin{\left(x \right)} = - \frac{1}{5}$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = - \frac{1}{5}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{5} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{5} \right)} + \pi$$
Или
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{5} \right)}$$
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{5} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

x1 = pi + asin(1/5)

$$x_{1} = \operatorname{asin}{\left(\frac{1}{5} \right)} + \pi$$

x2 = -asin(1/5)

$$x_{2} = - \operatorname{asin}{\left(\frac{1}{5} \right)}$$

Сумма и произведение корней

сумма

0 + pi + asin(1/5) - asin(1/5)

$$- \operatorname{asin}{\left(\frac{1}{5} \right)} + \left(0 + \left(\operatorname{asin}{\left(\frac{1}{5} \right)} + \pi\right)\right)$$

=

pi

$$\pi$$

произведение

1*(pi + asin(1/5))*-asin(1/5)

$$1 \left(\operatorname{asin}{\left(\frac{1}{5} \right)} + \pi\right) \left(- \operatorname{asin}{\left(\frac{1}{5} \right)}\right)$$

=

-(pi + asin(1/5))*asin(1/5)

$$- \left(\operatorname{asin}{\left(\frac{1}{5} \right)} + \pi\right) \operatorname{asin}{\left(\frac{1}{5} \right)}$$

Численный ответ

x1 = 3.34295057438012

x2 = -19.0509138423291

x3 = 72.4579889533556

x4 = 172.988953868229

x5 = -12.7677285351495

x6 = 18.6481980007484

x7 = -53.2057171902362

x8 = 31.2145686151076

x9 = 12.3650126935688

x10 = 75.1968657653647

x11 = -37.9004697638678

x12 = -50.466840378227

x13 = 129.006656717972

x14 = -65.7720878045953

x15 = -81.882766914125

x16 = 3845.10805007312

x17 = -72.0552731117749

x18 = 94.0464216869035

x19 = -59.4889024974157

x20 = 43.7809392294668

x21 = -28.0729759615178

x22 = -97.1880143404933

x23 = 87.7632363797239

x24 = -88.1659522213045

x25 = -15.5066053471586

x26 = 100.329606994083

x27 = -69.3163962997658

x28 = -100.732322835664

x29 = 37.4977539222872

x30 = -279.400388248701

x31 = 28.4756918030985

x32 = -9.22342003997905

x33 = -84.6216437261341

x34 = -107.015508142843

x35 = 91.3075448748943

x36 = 41.0420624174576

x37 = 4024.58154716932

x38 = 66.174803646176

x39 = 85.0243595677148

x40 = -56.7500256854066

x41 = 47.3252477246372

x42 = -75.5995816069454

x43 = -25.3340991495087

x44 = -44.1836550710474

x45 = 22.1925064959189

x46 = 225.993313137675

x47 = -40.639346575877

x48 = 6.08182738638926

x49 = 68.9136804581851

x50 = -34.3561612686974

x51 = -21.7897906543382

x52 = 97.5907301820739

x53 = 81.4800510725443

x54 = 9845.55001842962

x55 = 24.931383307928

x56 = 50.0641245366464

x57 = 15.9093211887393

x58 = -90.9048290333137

x59 = -6.48454322796992

x60 = -63.0332109925862

x61 = -78.3384584189545

x62 = -46.9225318830566

x63 = -2.94023473279946

x64 = 53.6084330318168

x65 = 78.7411742605352

x66 = 56.3473098438259

x67 = -31.6172844566883

x68 = 34.7588771102781

x69 = 59.8916183389964

x70 = 62.6304951510055

x71 = -0.201357920790331

x72 = -94.4491375284841

x73 = 9.62613588155971

График